This is the basic and conceptual question from polynomials in which we have given a equation (x^4+4x³-2x²-20x-15) and √5 and -√5 are its two zeroes and we have to find all the zeroes of the given polynomial.

RS Aggarwal, Class 10, chapter 2B, question no 18

let f(x)=x^4+4x³−2x²−20x−15

(x−√5)and(x−√5) are the factors of f(x)

and (x−√5)(x+√5)=(x²−5) is the factor of f(x)

Divide f(x) buy (x²−5) we get

set f(x)=0

x^4+4x³−2x²−20x−15=0

(x²−5)(x²+4x+3)=0

(x−√5)(x+√5)(x+1)(x+3)=0

x=√5 or x=−√5 or x=−1 or x=−3

hence all the zeros of the given polynomial are √5, −√5, −1 and −3.