Sir please give me a detailed solution of this question as it is taken from polynomials chapter in which we have given a equation (2x^4-3x³-5x²+9x-3) and √3 and -√3 are its two zeroes and we have to find all the zeroes of the given polynomial

RS Aggarwal, Class 10, chapter 2B, question no 17

Let f(x)=2x^4−3x³−5x²+9x−3

Given √3 and −√3 are the zeros of the polynomial.

(x−√3) and (x+√3) are factors f(x)

So (x−√3)(x+√3)=(x²−3) is a factor of f(x)

Divide f(x) by (x²−3)

set f(x)=0

(2x²−3x+1)(x²−3)=0

2x²−3x²−5x²+9x−3=0

(x²−3)(2x²−3x+1)=0

(x²−3)(2x²−2x−x+1)=0

(x−√3)(x+√3)(2x−1)(x−1)=0

either x=√3 or x=−√3 or x=1/2 or x=1

Hence , all the zeros of the given polynomial are √3, −√3, 1/2 and 1