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Find all the zeroes of the (2x^4-3x³-5x²+9x-3), if it is given that two of its zeroes are √3 and -√3

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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


1 Answer

  1. Let f(x)=2x^435+9x3

    Given √3 and −√3 are the zeros of the polynomial.
    (x−√3) and (x+√3) are factors f(x)
    So (x−√3)(x+√3)=(3) is a factor of f(x)
    Divide f(x) by (3)

    set f(x)=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

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