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 .

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Mathematics Class 10>Chapter 3 - Polynomials>Try This

Telangana Board Solutions for Chapter: Polynomials, Exercise 13: Try This

Author:Telangana Board

Telangana Board Mathematics Solutions for Exercise - Telangana Board Solutions for Chapter: Polynomials, Exercise 13: Try This

Attempt the practice questions on Chapter 3: Polynomials, Exercise 13: Try This with hints and solutions to strengthen your understanding. Mathematics Class 10 solutions are prepared by Experienced Embibe Experts.