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