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Find all the zeroes of the polynomial (2x^4-11x³+7x²+13x-7), it being given that two of its zeroes are (3+√2) and (3-√2)

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This is the basic and conceptual question from polynomials in which we have been asked to find all the zeroes of the polynomial if (3+√2) and (3-√2) are the zeroes of the polynomial (2x^4-11x³+7x²+13x-7).

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 2B, question no 19


1 Answer

  1. Let f(x)=2x^411+7+13x7

    Given : (3+√2) and (3−√2) are the zeroes of f(x)

    So (x(3+√2)) and (x(3−√2)) are factors of f(x)
    and (x(3+√2))(x(3−√2))=6x+7 is a factor of f(x)

    Divide f(x) by 6x+7 we get

    set f(x)=0
    x=3−√2 or x=3+√2 or x=1/2 or x=1

    hence all the zeros of the given polynomial are (3−√2), (3+√2), 1/2and 1.

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