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Find all the zeroes of the (x^4+x³-23x²-3x+60), if it is given that two of its zeroes are √3 and -√3

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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


1 Answer

  1. Let f(x)=x^4+233x+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 (3)

    Let f(x)=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.

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