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R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 10 Quadratic Equations

Chapter 10 – Quadratic Equations Exercise Ex. 10A

Question 1

Which of the following are quadratic equations in x?

(i)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

(i)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsis a quadratic polynomial

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations= 0 is a quadratic equation

Question 2

Which of the following are quadratic equations in x?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Clearly R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations is a quadratic polynomial

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsis a quadratic equation.

Question 3

Which of the following are quadratic equations in x?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations is a quadratic polynomial

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations = 0 is a quadratic equation

Question 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Clearly, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsis a quadratic equation

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsis a quadratic equation

Question 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsis not a quadratic polynomial since it containsR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations in which power R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations of x is not an integer.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsis not a quadratic equation

Question 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

And R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsBeing a polynomial of degree 2, it is a quadratic polynomial.

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsis a quadratic equation.

Question 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

And R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsbeing a polynomial of degree 3, it is not a quadratic polynomial

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsis not a quadratic equation

 

Question 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsis not a quadratic equation

Question 9

Which
of the following are quadratic equations in x?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Which
of the following are quadratic equations in x?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

Which
of the following are quadratic equations in x?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

Which of the following are the roots of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

(i) -1

(ii) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

(iii) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

The given equation is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

 

(i) On substituting x = -1 in the equation, we get

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

 

(ii) On substituting R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations in the equation, we get

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

(iii) On substituting R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations in the equation R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations, we get

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

Find the value of k for which x = 1 is a root of the equation R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

Since x = 1 is a solution of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsit must satisfy the equation.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Hence the required value of k = -4

Question 14

Find the value of a and b for which R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations and x = -2 are the roots of the equation R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

Since R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations is a root of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations, we haveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Again x = -2 being a root of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations, we have

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Multiplying (2) by 4 adding the result from (1), we get

11a = 44 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations a = 4

Putting a = 4 in (1), we get

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

Solve each of the following quadratic equations:

3R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations– 243 = 0

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, 9 and -9 are the roots of the equation R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 23

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 24

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of equationR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 25

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsand 1 are the roots of the equation R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations.

Question 26

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of the equation R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 27

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of the given equation R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 28

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of given equation

Question 29

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 31

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 31

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 32

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of the given equation

Question 33

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 33

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of the given equation

Question 34

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 34

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of the given equation

Question 35

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 35

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of the given equation

Question 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 38

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 38

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 41

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 41

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 42

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 42

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 43

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 43

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, 1 and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of the given equation

Question 44

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 44

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 45

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 45

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 46

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 46

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 47

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 47

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of the given equation

Question 48

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 48

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, 2 and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of given equation

Question 49

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 49

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 51

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 51

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 52

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 52

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 53

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 53

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 54

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 54

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 55

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 55

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 56

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 56

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of the given equation

Question 57

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 57

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 58

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 58

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of given equation

Question 59

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 59

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of given equation

Question 60

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 60

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of given equation

Question 61

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 61

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 62

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 62

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 63

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 63

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 64

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 64

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 65

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 65

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 66

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 66

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 67

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 67

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 68

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 68

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 69

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 69

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 70

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 70

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 71

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 71

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 72

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 72

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 73

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 73

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 74

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 74

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 75

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 75

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 76

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 76

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 77

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 77

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 78

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 78

Putting R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsthe given equation become

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Case I:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Case II:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of the given equation

Question 79

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 79

The given equation

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsis the roots of the given equation

Question 80

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 80

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 81

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 81

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, -2,0 are the roots of given equation

Question 82

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 82

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare the roots of given equation

Question 83

Solve the following quadratic equation:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 83

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, 3 and 2 are roots of the given equation

Chapter 10 – Quadratic Equations Exercise Ex. 10B

Question 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 10 – Quadratic Equations Exercise Ex. 10C

Question 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 31

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 31

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 33

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 33

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 34

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 34

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 35

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 35

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 38

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 38

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 41

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 41

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 10 – Quadratic Equations Exercise Ex. 10D

Question 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Show that the roots of the equation R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare real for all real values of p and q.

Solution 8

The given equation is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

This is the form of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Now R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations.

So, the roots of the given equation are real for all real value of p and q.

Question 9

For what values of k are the roots of the quadratic equation R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsreal and equal.

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 19

If the equation R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationshas equal roots , prove that R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

The given equation is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

For real and equal roots, we must have D = 0

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

If the roots of the equation R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsare real and equal, show that either a = 0 or R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 20

The given equation is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

For real and equal roots , we must have D =0

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 10 – Quadratic Equations Exercise Ex. 10E

Question 1

The sum of a natural number and its square is 156. Find the number.

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

The sum of a natural number and its positive square root is 132. Find the number.

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

The sum of two natural numbers is 28 and their product is 192. Find the numbers.

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

The sum of the squares of two consecutive positive integers is 365. Find the integers.

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

The sum of the squares of two consecutive positive odd numbers is 514. Find the numbers.

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

The product of two consecutive positive integers is 306. Find the integers.

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Two numbers differ by 3 and their product is 504. Find the numbers.

Solution 8

Let the required number be x and x – 3, then

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, the required numbers are (24,21) or (-21 and-24)

Question 9

Find two consecutive multiples of 3 whose product is 648.

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Find two consecutive positive odd integers whose product is 483.

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

Find two consecutive positive even integers whose product is 288.

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

The sum of the squares of two consecutive multiples of 7 is 1225. Find the multiples.

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 18

Divide 57 into two parts whose product is 680.

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.

Solution 20

Let the smaller part and larger part be x, 16 – x

Then,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

-42 is not a positive part

Hence, the larger and smaller parts are 10, 6 respectively

Question 21

Find two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.

Solution 21

Let the required number be x and y, hen

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 22

The difference of the squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

Solution 22

Let x, y be the two natural numbers and x > y

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations——(1)

Also, square of smaller number = 4 larger number

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations———(2)

Putting value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsfrom (1), we get

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Thus, the two required numbers are 9 and 6

Question 23

Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46, find the integers.

Solution 23

Let the three consecutive numbers be x, x + 1, x + 2

Sum of square of first and product of the other two

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsRequired numbers are 4, 5 and 6

Question 24

A two-digit number is 4 times the sum of its digits and twice the product of its digits. Find the numbers.

Solution 24

Let the tens digit be x and units digit be y

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, the tens digit is 3 and units digit is (2 3) is

Hence the required number is 36

Question 25

A two-digit number is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places. Find the number.

Solution 25

Let the tens digit and units digits of the required number be x and y respectively

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

The ten digit is 2 and unit digit is 7

Hence, the required number is 27

Question 26

The denominator of a fraction is 3 more than its numerator. The sum of the fraction and its reciprocal isR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations. Find the fraction.

Solution 26

Let the numerator and denominator be x, x + 3

Then,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, numerator and denominator are 2 and 5 respectively and fraction is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 29

A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left. When he increased the size of the square by one student, he found he was short of 25 students. Find the number of students.

Solution 29

Let there be x rows and number of student in each row be x

Then, total number of students = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence total number of student

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Total number of students is 600

Question 30

300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.

Solution 30

Let the number of students be x, then

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence the number of students is 50

Question 31

In a class test, the sum of Kamal’s marks in Mathematics and English is 40. Had he got 3 marks more in Mathematics and 4 marks less in English, the product of the marks would have been 360. Find his marks in two subjects separately.

Solution 31

Let the marks obtained by Kamal in Mathematics and English be x and y

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

The marks obtained by Kamal in Mathematics and English respectively are (21,19) or (12,28)

Question 32

Some students planned a picnic. The total budget for food was Rs.2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by Rs.20. How many students attended the picnic and how much did each student pay for the food?

Solution 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 33

If the price of a book is reduced by Rs.5, a person can buy 4 more books for Rs.600. Find the original price of the book.

Solution 33

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 34

A person on tour has Rs.10800 for his expenses. If he extends his tour by 4 days, he has to cut down his daily expenses by Rs.90. Find the original duration of the tour.

Solution 34

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 35

In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained by him in the two subjects separately.

Solution 35

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 36

A man buys a number of pens for Rs.180. If he had bought 3 more pens for the same amount, each pen would have cost him Rs.3 less. How many pens did he buy?

Solution 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 37

A dealer sells an article for Rs.75 and gains as much per cent as the cost price of the article. Find the cost price of the article.

Solution 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 38

One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Find their present ages.

Solution 38

Let the age of son be x and age of man = y

1 year ago

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 40

The sum of the ages of a boy and his brother is 25 years and the product of their ages in years is 126.Find their ages.

Solution 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 41

The product of Meena’s age 5 years ago and her age 8 years later is 30. Find her present age.

Solution 41

Let the present age of Meena be x

Then,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence the present age of Meena is 7 years

Question 42

Two years ago, a man’s age was three times the square of his son’s age. In three years time, his age will be four times his son’s age. Find their present ages.

Solution 42

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 43

A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.

Solution 43

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 44

While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalise the injured and so the plane started late by 30 minutes. To reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hour. Find the original speed of the plane.

Do you appreciate the values shown by the pilot, namely promptness in providing help to the injured and his efforts to reach in time?

Solution 44

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 45

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.

Solution 45

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 46

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

Solution 46

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 47

A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Solution 47

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 48

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 kmph more, it would have taken 30 minutes less for the journey. Find the original speed of the train.

Solution 48

Let the original speed of the train be x km.hour

Then speed increases by 15 km/ph = (x + 15)km/hours

Then time taken at original speed = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Then, time taken at in increased speed = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsDifference between the two lines taken R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Then, original speed of the train = 45km / h

Question 49

A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find its usual speed.

Solution 49

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 50

The distance between Mumbai and Pune is 192 km. Travelling by the Deccan Queen, it takes 48 minutes less than another train. Calculate the speed of the Deccan Queen if the speeds of the two trains differ by 20 kmph.

Solution 50

Let the speed of the Deccan Queen = x kmph

The, speed of other train = (x – 20)kmph

Then, time taken by Deccan Queen = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Time taken by other train = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Difference of time taken by two trains is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, speed of Deccan Queen = 80km/h

Question 51

A motorboat whose speed is 18 km per hour in still water takes 1 hour more to go 24 km upstream than to return to the same point. Find the speed of the stream.

Solution 51

Let the speed of stream be x km/h

Speed of boat in still stream = 18 km/h

Speed of boat up the stream = 18 – x km/h

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsTime taken by boat to go up the stream 24 km = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsTime taken by boat to go down the stream = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Time taken by the boat to go up the stream is 1 hour more that the time taken down the stream

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsSpeed of the stream = 6 km/h

Question 52

The speed of a boat in still water is 8 kmph. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

Solution 52

Let the speed of the stream be x kmph

Then the speed of boat down stream = (8 + x) kmph

And the speed of boat upstream = (8 – x)kmph

Time taken to cover 15 km upstream = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Time taken to cover 22 km downstream = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Total time taken = 5 hours

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, the speed of stream is 3 kmph

Question 53

A motorboat whose speed is 9 km/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream.

Solution 53

Let the speed of the stream be = x km/h

Speed of boat in still waters = 9 km/h

Speed of boat down stream = 9 + x

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationstime taken by boat to go 15 km downstream = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Speed of boat upstream = 9 – x

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationstime taken by boat to go 15 km of stream = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 54

A takes 10 days less than time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.

Solution 54

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 55

Two pipes running together can fill a cistern inR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsminutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.

Solution 55

Let the faster pipe takes x minutes to fill the cistern

Then, the other pipe takes (x + 3) minute

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

The faster pipe takes 5 minutes to fill the cistern

Then, the other pipe takes (5 + 3) minutes = 8 minutes

Question 56

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 56

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 57

Two water taps together can fill a tank in 6 hours. The tap of larger diameter takes 9 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Solution 57

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 58

The length of rectangle is twice its breadth and its area is 288 sq.cm. Find the dimensions of the rectangle.

Solution 58

Let the breadth of a rectangle = x cm

Then, length of the rectangle = 2x cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Thus, breadth of rectangle = 12 cm

And length of rectangle = (2 12) = 24 cm

Question 59

The length of a rectangular field is three times its breadth. If the area of the field be 147 sq.m, find the length of the field.

Solution 59

Let the breadth of a rectangle = x meter

Then, length of rectangle = 3x meter

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Thus, breadth of rectangle = 7 m

And length of rectangle = (3 7)m = 21 m

Question 60

The length of a hall is 3 metres more than its breadth. If the area of the hall is 238 sq.m, calculate its length and breadth.

Solution 60

Let the breadth of hall = x meters

Then, length of the hall = (x + 3) meters

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsArea = length breadth = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Thus, the breadth of hall is 14 cm

And length of the hall is (14 + 3) = 17 cm

Question 61

The perimeter of a rectangular plot is 62 m and its area is 228 sq. metres. Find the dimensions of the plot.

Solution 61

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 62

A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 120 m2. Find the width of the path.

Solution 62

Let the width of the path be x meters,

Then,

Area of path = 16 10 – (16 – 2x) (10 – 2x) = 120

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence the required width is 3 meter as x cannot be 10m

Question 63

The sum of the areas of two squares is 640 m2. If the difference in their perimeters be 64 m, find the sides of the two squares.

Solution 63

Let x and y  be the lengths of the two square fields.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

4x – 4y = 64

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationsx – y = 16——(2)

From (2),

x = y + 16,

Putting value of x in (1)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsSides of two squares are 24m and 8m respectively

Question 64

The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 cm more than the width of the rectangle. Their areas being equal, find their dimensions.

Solution 64

Let the side of square be x cm

Then, length of the rectangle = 3x cm

Breadth of the rectangle = (x – 4) cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsArea of rectangle = Area of square x

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Thus, side of the square = 6 cm

And length of the rectangle = (3 6) = 18 cm

Then, breadth of the rectangle = (6 – 4) cm = 2 cm

Question 65

A farmer prepares a rectangular vegetable garden of area 180 sq. m. With 39 metres of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden.

Solution 65

Let the length = x meter

Area = length breadth = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

If ength of the rectangle = 15 m

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Also, if length of rectangle = 24 m

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 66

The area of a right triangle is 600 cm2. If the base of the triangle exceeds the altitude by 10 cm, find the dimensions of the triangle.

Solution 66

Let the altitude of triangle be x cm

Then, base of triangle is (x + 10) cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, altitude of triangle is 30 cm and base of triangle 40 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 67

The area of a right-angled triangle is 96 sq m. If the base is three times the altitude, find the base.

Solution 67

Let the altitude of triangle be x meter

Hence, base = 3x meter

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Hence, altitude of triangle is 8 cm

And base of triangle = 3x = (3 8) cm = 24 cm

Question 68

The area of a right-angled triangle is 165 sq m. Determine its base and altitude if the latter exceeds the former by 7 metres.

Solution 68

Let the base of triangle be x meter

Then, altitude of triangle = (x + 7) meter

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Thus, the base of the triangle = 15 m

And the altitude of triangle = (15 + 7) = 22 m

Question 69

The hypotenuse of a right-angled triangle is 20 metres. If the difference between the lengths of the other sides be 4 m, find the other sides.

Solution 69

Let the other sides of triangle be x and (x -4) meters

By Pythagoras theorem, we have

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Thus, height of triangle be = 16 cm

And the base of the triangle = (16 – 4) = 12 cm

Question 70

The length of the hypotenuse of a right-angled triangle exceeds the length of the base by 2 cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle.

Solution 70

Let the base of the triangle be x

Then, hypotenuse = (x + 2) cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Thus, base of triangle = 15 cm

Then, hypotenuse of triangle = (15 +2 )= 17 cm

And altitude of triangle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 71

The hypotenuse of a right-angled triangle is 1 metre less than twice the shortest side. If the third side is 1 metre more than the shortest side, find the sides of the triangle.

Solution 71

Let the shorter side of triangle be x meter

Then, its hypotenuse = (2x – 1)meter

And let the altitude = (x + 1) meter

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 10 – Quadratic Equations Exercise Ex. 10F

Question 1

Which
of the following is a quadratic equation?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Which
of the following is a quadratic equation?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Which
of the following is not a quadratic equation?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

(a) Real
and equal

(b) Real
and unequal

(c) Imaginary

(d) None
of these

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

(a) Real,
unequal and rational

(b) Real,
unequal and irrational

(c) Real
and equal

(d) Imaginary

Solution 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

(a) Real,
unequal and rational

(b) Real,
unequal and irrational

(c) Real
and equal

(d) Imaginary

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 29

The
perimeter of a rectangle is 82 m and its area is 400 m2. The
breadth of the rectangle is

(a) 25
m

(b) 20
m

(c) 16
m

(d) 9
m

Solution 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 30

The
length of a rectangular field exceeds its breadth by 8 m and the area of the
field is 240 m2. The breadth of the field is

(a) 20
m

(b) 30
m

(c) 12
m

(d) 16
m

Solution 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 31

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 31

Question 32

The
sum of two natural numbers is 8 and their product is 15. Find the numbers.

Solution 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 33

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 33

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 34

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 34

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 35

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 35

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 38

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 38

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 41

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 41

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 42

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 42

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 43

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 43

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 44

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 44

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 45

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 45

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 46

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 46

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 47

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 47

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 48

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 48

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 49

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 49

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 51

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 51

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 52

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 52

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 53

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 53

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 54

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 54

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 55

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 55

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

 

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