Find a quadratic polynomial with zeroes - 2 and 1 3 .

Let the quadratic polynomial be a x 2 + b x + c , a ≠ 0 and its zero be α and β . Here, α = - 2 and β = 1 3 Sum of the zeroes = α + β = - 2 + 1 3 = - 5 3 Product of the zeroes = α β = - 2 × 1 3 = - 2 3 The required quadratic polynomial a x 2 + b x + c is k x 2 - α + β x + α β where k is constant and k ≠ 0 So, we have, k x 2 - - 5 3 x - 2 3 We can take different value for k . When k = 3 , the quadratic polynomial is 3 x 2 + 5 x - 2 .

What is the quadratic polynomial the sum of whose zeroes is - 3 2 and the product of the zeroes is - 1 .

We can find the quadratic equation if we know the sum of the roots and product of the roots. We have, f x = x 2 - α + β x + α β , where α , β are the roots of the quadratic polynomial. Given, sum of the roots α + β = - 3 2 and product of the roots α β = - 1 So, we get f x = k x 2 - - 3 2 x - 1 For k = 2 ; f x = 2 x 2 + 3 x - 2 Hence, the required quadratic polynomial is 2 x 2 + 3 x - 2 .

E M B I B E

Mathematics Class 10>Chapter 3 - Polynomials>Do This>Q (ii)

EASY

10th Telangana Board

IMPORTANT

Earn 100

Find the zeroes of the quadratic polynomial given below. Find the sum and product of the zeroes and verify relationship to the coefficient of terms in the polynomial.

$p (x) = x^{2} - 4 x + 3$

Important Questions on Polynomials

EASY

10th Telangana Board

IMPORTANT

Mathematics Class 10>Chapter 3 - Polynomials>Do This>Q (iii)

Find the zeroes of the quadratic polynomial given below. Find the sum and product of the zeroes and verify relationship to the coefficient of terms in the polynomial.

$p (x) = x^{2} - 4$

EASY

10th Telangana Board

IMPORTANT

Mathematics Class 10>Chapter 3 - Polynomials>Do This>Q (iv)

Find the zeroes of the quadratic polynomial given below. Find the sum and product of the zeroes and verify relationship to the coefficient of terms in the polynomial.

$p (x) = x^{2} + 2 x + 1$

MEDIUM

10th Telangana Board

IMPORTANT

Mathematics Class 10>Chapter 3 - Polynomials>Try This>Q (i)

Find a quadratic polynomial with zeroes