We have given a quadratic polynomial f(x)=x³-3x²+x+1 and (a-b), a and (a+b) are the zeroes of the given polynomial and we have been asked to find the value of a and b.

This question is taken from polynomials and it is already asked in various examinations

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 2C, question no 25

a−b, a, a+b are zeroes of x³−3x²+x+1

⇒a−b+a+a+b= sum of zeroes = 3

⇒3a=3

⇒a=1

(a−b)(a)(a+b)= product of zeroes =−1

⇒(1−b)(1+b)=−1

⇒1−b²=−1

⇒b²=2

⇒b=±√2