Find the polynomial whose zeroes are α = 1 2 , β = 1 2 .

Given: α = 1 2 , β = 1 2 Let us consider the polynomial p ( x ) = a x 2 + b x + c with zeroes α , β . Sum of zeroes = α + β = 1 2 + 1 2 = 1 Sum of zeroes = - b a ⇒ 1 = - - 1 1 = - b a Product of zeroes = α β = 1 2 × 1 2 = 1 4 Product of zeroes = c a ⇒ 1 4 = 1 4 1 = c a Comparing with the coefficients, we get, a = 1 , b = - 1 , c = 1 4 . The polynomial formed = a x 2 + b x + c = x 2 - x + 1 4 Hence, one of the polynomial with α = 1 2 , β = 1 2 is p x = x 2 - x + 1 4 . The other polynomials are, p x = k x 2 - x + 1 4 .

Find the polynomial whose zeroes are α = - 5 3 , β = - 5 3 .

Given: α = - 5 3 , β = - 5 3 Let us consider the polynomial p ( x ) = a x 2 + b x + c with zeroes α , β . Sum of zeroes = α + β = - 5 3 + - 5 3 = - 10 3 Sum of zeroes = - b a ⇒ - 10 3 = - b a Product of zeroes = α β = - 5 3 × - 5 3 = 25 9 Product of zeroes = c a ⇒ 25 9 = 25 3 3 = c a Comparing with the coefficients, we get, a = 3 , b = 10 , c = 25 3 . The polynomial formed = a x 2 + b x + c = 3 x 2 + 10 x + 25 3 Hence, one of the polynomial with α = - 5 3 , β = - 5 3 is p x = 3 x 2 + 10 x + 25 3 . The other polynomials are, p x = k 3 x 2 + 10 x + 25 3 .

E M B I B E

New Mathematics for Class X>Chapter 2 - Polynomials>EXERCISE

H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Polynomials, Exercise 2: EXERCISE

Author:H K Dass, Rama Verma & Bhagwat Swarup Sharma

H K Dass Mathematics Solutions for Exercise - H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Polynomials, Exercise 2: EXERCISE

Attempt the free practice questions on Chapter 2: Polynomials, Exercise 2: EXERCISE with hints and solutions to strengthen your understanding. New Mathematics for Class X solutions are prepared by Experienced Embibe Experts.