Exercise 2.2

Question 1

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i)

Sol :

or

or

Therefore , the zeroes of are 4 and -2 .

Sum of zeroes

Product of zeroes

(ii)

Sol :

Therefore , the zeroes of are and

Sum of zeroes

Product of zeroes

(iii)

Sol :

or

or

Therefore , the zeroes of are and

Sum of zeroes

Product of zeroes

(iv)

Sol :

or

or

Therefore , the zeroes of are 0 and – 2 .

Sum of zeroes

Product of zeroes

(v)

Sol :

or

or

Therefore , the zeroes of are and

Sum of zeroes

Product of zeroes

(vi)

Sol :

or

or

Therefore , the zeroes of are and

Sum of zeroes

Product of zeroes

Concept insight: The zero of a polynomial is that value of the variable which when substituted in the polynomial makes its value 0.

When a quadratic polynomial is equated to 0, then the values of the variable obtained are the zeroes of that polynomial. The relationship between the zeroes of a quadratic polynomial with its coefficients is very important. Also, while verifying the above relationships, be careful about the signs of the coefficients.

(working)

Question 2

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

(i)

(ii)

(iii)

(iv) 1 , 1

(v)

(vi) 4 , 1

Let the polynomial be , and its zeroes be and .

Therefore, the quadratic polynomial is 4x2 − x − 4.

Let the polynomial be , and its zeroes be and .

Therefore, the quadratic polynomial is 3x2 − x + 1.

Let the polynomial be , and its zeroes be and .

Therefore, the quadratic polynomial is .

Let the polynomial be , and its zeroes be and .

Therefore, the quadratic polynomial is .

Let the polynomial be , and its zeroes be and .

Therefore, the quadratic polynomial is .

Let the polynomial be .