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R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 2 Polynomials

 

Chapter 2 – Polynomials Exercise Ex. 2A


Question 1

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients: x2 + 7x + 12

Solution 1

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


Question 2

Find the zeros of the following quadratic polynomials and verify the relationship
between the zeros and the coefficients: x2 – 2x – 8

Solution 2

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


Question 3

Find the zeros of the quadratic polynomial (x2 + 3x – 10) and verify the relation between its zeros and coefficients.

Solution 3

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


Question 4

Find the zeros of the quadratic polynomial (4x2 – 4x – 3) and verify the relation between its zeros and coefficients.

Solution 4

We have

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


Question 5

Find the zeros of the quadratic polynomial (5x2 – 4 – 8x) and verify the relationship between its zeros and coefficients of the given polynomial.

Solution 5

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


Question 6

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients: R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials

Solution 6

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

 


Question 7

Find the zeros of the quadratic polynomial (2x2 – 11x + 15) and verify the relation between its zeros and coefficients.

Solution 7

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


Question 8

Find the zeros of the following quadratic polynomials and verify the relationship

between the zeros and the coefficients: 4x2 – 4x + 1

Solution 8

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


Question 9

Find the zeros of the quadratic polynomial (x2 – 5) and verify the relation between its zeros and coefficients.

Solution 9

We have

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

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

So the zeros of f(x) are R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomialsand R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials

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


Question 10

Find the zeros of the quadratic polynomial (8x2 – 4) and verify the relation between its zeros and coefficients.

Solution 10

Let

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

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


Question 11

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients: 5y2 + 10y

Solution 11

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

 


Question 12

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients: 3x2 – x – 4

Solution 12

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


Question 13

Find the quadratic polynomial whose zeros are 2 and -6. Verify the relation between the coefficients and the zeros of the polynomial.

Solution 13

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


Question 14

Find the quadratic polynomial whose zeros are R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials. Verify the relation between the coefficients and the zeros of the polynomial.

Solution 14

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


Question 15

Find the quadratic polynomial, sum of whose zeros is 8 and their product is 12. Hence, find the zeros of the polynomial.

Solution 15

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

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


Question 16

Find the quadratic polynomial, sum of whose zeros is 0 and their product is -1. Hence, find the zeros of the polynomial.

Solution 16

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


Question 17

Find the quadratic polynomial, sum of whose zeros is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials and their product is 1. Hence, find the zeros of the polynomial.

Solution 17

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


Question 18

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

Solution 18

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


Question 19

If x =R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomialsand x = -3 are the roots of the quadratic equation ax2 + 7x + b = 0 then find the values of a and b.

Solution 19

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


Question 20

If (x + a) is a factor of the polynomial 2x2 + 2ax + 5x + 10, find the value of a.

Solution 20

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


Question 21

One zero of the polynomial 3x3 + 16x2 + 15x – 18 is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - PolynomialsFind the other zeros of the polynomial.

Solution 21

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


Chapter 2 – Polynomials Exercise Ex. 2B

Question 1

Verify that 3, -2, 1 are the zeros of the cubic polynomial p(x) = x3 – 2x2 – 5x + 6 and verify the relation between its zeros and coefficients.

Solution 1
R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials
Question 2

Verify that R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials are the zeros of the cubic polynomial p(x) = 3x3 – 10x2 – 27x + 10 and verify the relation between its zeros and coefficients.

Solution 2

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

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


Question 3

Find a cubic polynomial whose zeros are 2, -3 and 4.

Solution 3

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


Question 4

Find a cubic polynomial whose zeros are R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials1 and -3.
Solution 4

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


Question 5

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and the product of its zeros as 5, -2 and -24 respectively.

Solution 5

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


Question 6

Find the quotient and the remainder when: f(x) = x3 – 3x2 + 5x – 3 is divided by g(x)= x2 – 2.

Solution 6

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


Question 7

Find the quotient and the remainder when: f(x)= x4 -3x2 + 4x + 5 is divided by g(x)= x2 + 1 – x.

Solution 7

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


Question 8

Find the quotient and the remainder when: f(x)= x4 – 5x + 6 is divided by g(x) = 2 – x2.

Solution 8

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


Question 9

By actual division, show that x2 – 3 is a factor of 2x4 + 3x3 – 2x2 – 9x – 12.

Solution 9

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


Question 10

On dividing 3x3 + x2 + 2x + 5 by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).

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

Solution 10

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


Question 11

Verify division algorithm for the polynomials f(x) = 8 + 20x + x2 – 6x3 and g(x) = 2 + 5x – 3x2.

Solution 11

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


Question 12

It is given that -1 is one of the zeros of the polynomial x3 + 2x2 – 11x – 12. Find all the zeros of the given polynomial.

Solution 12

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


Question 13

If 1 and -2 are two zeros of the polynomialR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials, find its third zero.

Solution 13

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


Question 14

If 3 and -3 are two zeros of the polynomialR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials, find all the zeroes of the given polynomial.
Solution 14

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


Question 15

If 2 and -2 are two zeros of the polynomialR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials, find all the zeros of the given Polynomial.
Solution 15

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


Question 16

Find all the zeros ofR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials, if it is given that two of its zeros are R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials
Solution 16

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


Question 17

Find all the zeros ofR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials, it being given that two of its zeros are R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials
Solution 17

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

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


Question 18

Obtain all other zeros of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials, if two of its zeros are R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials.

Solution 18

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

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


Question 19

Find all the zeros of the polynomial R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials, it being given that two of its zeros are R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials.

Solution 19

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


Chapter 2 – Polynomials Exercise Ex. 2C

Question 1

If one zero of the polynomial x2 – 4x + 1 is (2 +R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials), write the other zero.

Solution 1

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

Question 2

Find
the zeros of the polynomial x2 + x – p(p
+ 1).

Solution 2

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

Question 3

Find
the zeros of the polynomial x2 – 3x – m(m
+ 3).

Solution 3

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


Question 4

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

Solution 4

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


Question 5

If one zero of the quadratic polynomial kx2 + 3x + k is 2 then find
the value of k.

Solution 5

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


Question 6

If 3 is a zero of the polynomial 2x2 + x + k, find the value of k.

Solution 6

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


Question 7

If -4 is a zero of the polynomial x2 – x – (2k + 2) then find the
value of k.

Solution 7

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


Question 8

If 1 is a zero of the polynomial ax2 – 3(a – 1)x – 1 then find the value of a.

Solution 8

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


Question 9

If -2 is a zero of the polynomial 3x2 + 4x + 2k then find the value of k.

Solution 9

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


Question 10

Write the zeros of the polynomial x2 – x – 6.

Solution 10

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


Question 11

If the sum of the zeros of the quadratic polynomial kx2 – 3x + 5 is 1, write the value of k.

Solution 11

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


Question 12

If the product of the zeros of the quadratic polynomial x2 – 4x + k is 3 then write the value of k.

Solution 12

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


Question 13

If (x + a) is a factor of (2x2 + 2ax + 5x + 10), find the value of a.

Solution 13

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


Question 14

If (a – b), a and (a + b) are zeros of the polynomial 2x3 – 6x2 + 5x – 7, write the value of a.

Solution 14

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


Question 15

If x3 + x2 – ax + b is divisible by (x2 – x), write the values of a and b.

Solution 15

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


Question 16

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

Solution 16

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


Question 17

State division algorithm for polynomials.

Solution 17

If f(x) and g(x) are any two polynomials with g(x) ≠ 0,
then we can always find polynomials q(x) and r(x) such that f(x) = q(x)g(x) + r(x),

where r(x) = 0
or degree r(x) < degree g(x).


Question 18

The sum of the zeros and the product of zeros of a quadratic polynomial are R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomialsand -3 respectively. Write the polynomial.
Solution 18

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


Question 19

Write the zeros of the quadratic polynomial f(x) = 6x2 – 3.

Solution 19

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


Question 20

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

Solution 20

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


Question 21

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

Solution 21

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


Question 22

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

Solution 22

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


Question 23

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

Solution 23

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


Question 24

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

Solution 24

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


Question 25

If the zeros of the polynomial f(x) = x3 – 3x2 + x + 1 are (a – b), a and (a + b), find a and b.

Solution 25

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


Chapter 2 – Polynomials Exercise FA


Question 1

Zeros of p(x) = x2 – 2x – 3 are

(a) 1, -3

(b) 3, -1

(c) -3, -1

(d)1, 3

Solution 1

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


Question 2

If 𝛼, 𝛽, 𝛾 are the zeros of the polynomial x3 – 6x2 – x + 30, then (𝛼𝛽 + 𝛽𝛾 + 𝛾𝛼) = ?

(a) -1

(b) 1

(c) -5

(d)30

Solution 2

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


Question 3

If 𝛼, 𝛽 are the zeros of kx2 – 2x + 3k such that 𝛼 + 𝛽 = 𝛼𝛽, then k = ?

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

Solution 3

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


Question 4

It is given that the difference between the zeros of 4x2 – 8kx + 9 is 4 and k > 0. Then, k = ?

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

Solution 4

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


Question 5

Find the zeros of the polynomial x2 + 2x – 195.

Solution 5

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


Question 6

If one zeros of the polynomial (a2 + 9)x2 + 13x + 6a is the reciprocal of the other, find the value of a.

Solution 6

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


Question 7

Find a quadratic polynomial whose zeros are 2 and -5.

Solution 7

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


Question 8

If the zeros of the polynomial x3 – 3x2 + x + 1 are (a – b), a and (a + b), find the values of a and b.

Solution 8

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


Question 9

Verify that 2 is a zero of the polynomial x3 + 4x2 – 3x – 18.

Solution 9

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


Question 10

Find the quadratic polynomial, the sum of whose zeros is -5 and their product is 6.

Solution 10

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


Question 11

Find a cubic polynomial whose zeros are 3, 5 and -2.

Solution 11

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


Question 12

Using remainder theorem, find the remainder
when p(x) = x3 + 3x2 – 5x + 4 is divided by (x – 2).

Solution 12

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


Question 13

Show that (x + 2) is a factor of f(x) = x3 + 4x2 + x – 6.

Solution 13

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


Question 14

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

Solution 14

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


Question 15

If 𝛼, 𝛽 are the zeros of the polynomial f(x) = x2 – 5x + k such that 𝛼𝛽 = 1, find the value of k.

Solution 15

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


Question 16

Show that the polynomial f(x) = x4 + 4x2 + 6 has no zero.

Solution 16

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

Question 17

If one zero of the polynomial p(x) = x3
– 6x2 + 11x – 6 is 3, find the other two zeros.

Solution 17

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


Question 18

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

Solution 18

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


Question 19

Find the quotient when p(x) = 3x4 + 5x3 – 7x2 + 2x + 2 is divided by (x2 + 3x + 1).

Solution 19

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


Question 20

Use remainder theorem to find the value of
k, it being given that when x3 + 2x2 + kx + 3 is
divided by (x – 3), then the remainder is 21.

Solution 20

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

Chapter 2 – Polynomials Exercise MCQ


Question 1

Which of the following is a polynomial?

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

Solution 1

Correct answer: (d)

An expression of the form p(x) = a0 + a1x + a2x2 + ….. + anxn, where an ≠ 0, is called a polynomial in x of degree n.

Here, a0, a1, a2, ……, an are real numbers and each power of x is a non-negative integer.

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


Question 2

Which of the following is not a polynomial?

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

Solution 2

Correct answer: (d)

An expression of the form p(x) = a0 + a1x + a2x2 + ….. + anxn, where an ≠ 0, is called a polynomial in x of degree n.

Here, a0, a1, a2, ……, an are real numbers and each power of x is a non-negative integer.

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


Question 3

The zeros of the polynomial x2 – 2x – 3 are

(a)-3, 1

(b)-3, -1

(c) 3, -1

(d) 3, 1

Solution 3

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


Question 4

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

Solution 4

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

Question 5

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

Solution 5

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


Question 6

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

Solution 6

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


Question 7

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

Solution 7

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

Question 8

The sum and the product of the zeros of a quadratic polynomial are 3 and -10 respectively. The quadratic polynomial is

(a) x2 – 3x + 10

(b) x2 + 3x – 10

(c) x2 – 3x – 10

(d) x2 + 3x + 10

Solution 8

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


Question 9

A quadratic polynomial whose zeros are 5 and -3, is

(a) x2 + 2x – 15

(b) x2 – 2x + 15

(c) x2 – 2x – 15

(d)none of these

Solution 9

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


Question 10

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

(a) 10x2 +x + 3

(b) 10x2 + x – 3

(c) 10x2 – x + 3

(d) 10x2 – x – 3

Solution 10

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


Question 11

The zeros of the quadratic polynomial x2 + 88x + 125 are

(a) both positive

(b) both negative

(c) one positive and one negative

(d) both equal

Solution 11

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


Question 12

If 𝛼 and 𝛽 are the zeroes of x2 + 5x + 8 then the value of (𝛼 + 𝛽) is

(a) 5

(b) -5

(c) 8

(d) -8

Solution 12

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


Question 13

If 𝛼 and 𝛽 are the zeros of 2x2 + 5x – 9 then the value of 𝛼𝛽 is

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

Solution 13

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


Question 14

If one zero of the quadratic polynomial kx2 + 3x + k is 2 then the value of k is

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

Solution 14

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


Question 15

If one zero of the quadratic polynomial (k – 1)x2 + kx + 1 is -4, then the value of k is

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

Solution 15

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


Question 16

If -2 and 3 are the zeros of the quadratic polynomial x2 + (a + 1)x + b then

(a) a = -2, b = 6

(b) a = 2, b = -6

(c) a = -2, b = -6

(d) a = 2, b = 6

Solution 16

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


Question 17

If one zero of 3x2 + 8x + k be the reciprocal of the other then k = ?

(a) 3

(b) -3

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials

(d)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials

Solution 17

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


Question 18

If the sum of the zeros of the quadratic polynomial kx2 + 2x + 3k is equal to the product of its zeros then k = ?

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

Solution 18

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


Question 19

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

(a) 3

(b) -3

(c) 12

(d)-12

Solution 19

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


Question 20

If 𝛼, 𝛽, 𝛾 are the zeros of the polynomial x3 – 6x2 – x + 30, then (𝛼𝛽 + 𝛽𝛾 + 𝛾𝛼) = ?

(a) -1

(b) 1

(c) -5

(d)30

Solution 20

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


Question 21

If 𝛼, 𝛽, 𝛾 be the zeros of the polynomial 2x3 + x2 – 13x + 6, then 𝛼𝛽𝛾

(a) -3

(b) 3

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Polynomials

Solution 21

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


Question 22

If 𝛼, 𝛽, 𝛾 be the zeros of the polynomial p(x) such that (𝛼 + 𝛽 + 𝛾) = 3, (𝛼𝛽 + 𝛽𝛾 + 𝛾𝛼) = -10 and 𝛼𝛽𝛾 = -24, then p(x) =?

(a) x3 + 3x2 – 10x + 24

(b) x3 + 3x2 + 10x – 24

(c) x3 – 3x2 – 10x + 24

(d) None of these

Solution 22

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


Question 23

If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are 0, then the third zero is

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

Solution 23

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


Question 24

If one of the zeros of the cubic polynomial ax3 + bx2 + cx + d is 0, then the product of other two zeros are

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

Solution 24

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


Question 25

If one of the zeros of the cubic polynomial x3 + ax2 + bx + c is -1, then the product of the other two zeros is

(a) a – b – 1

(b) b – a – 1

(c) 1 – a + b

(d) 1 + a – b

Solution 25

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

Question 26

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

(a) 3

(b) -3

(c) -2

(d) 2

Solution 26

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


Question 27

On dividing a polynomial p(x) by a non-zero polynomial q(x), let g(x) be the quotient and r(x) be the remainder, then p(x) = q(x).g(x) + r(x), where

(a)r(x) = 0 always

(b)deg r(x) < deg g(x) always

(c) either r(x) = 0 or deg r(x) < deg g(x)

(d) r(x) = g(x)

Solution 27

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


Question 28

Which of the following is a true statement?

(a)x2 + 5x – 3 is a linear polynomial

(b)x2 + 4x – 1 is a binomial

(c) x + 1 is a monomial

(d) 5x3 is a monomial

 

Solution 28

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


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