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Rajan@2021
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Obtain all other zeroes of (x^4+4x³-2x²-20x-15) if two of its zeroes are √5 and -√5.

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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

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  1. let f(x)=x^4+4220x15
    (x−√5)and(x−√5) are the factors of f(x)
    and (x−√5)(x+√5)=(5) is the factor of f(x)
    Divide f(x) buy (5) we get

    set f(x)=0

    x^4+4220x15=0
    (5)(+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.

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