One of the most important and exam oriented question from polynomials in which we have given a equation (x^4+x³-23x²-3x+60) and it is also given that √3 and -√3 are its two zeroes and we have been asked to calculate all the zeroes of the given polynomial

RS Aggarwal, Class 10, chapter 2B, question no 16

## Let f(x)=x^4+x³−23x²−3x+60

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

(x−√3) and (x−√3) are factors of f(x)

Divide f(x) by (x²−3)

Let f(x)=0

(x²+x−20)(x²−3)=0

⇒(x2+5x−4x−20)(x²−3)=0

⇒[x(x+5)−4(x+5)](x²−3)=0

⇒(x−4)(x+5)(x+√3)(x−√3)=0

Either x=4 or x=−5 or x=√3 or x=−√3

hence all the zeros of the given polynomial are √3, −√3, 4 and −5.