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10 August, 18:59

Find all the zeroes of the polynomial p (x) = x4 - 7x³ + 9x² + 13x - 4, if two of its zeroes are (2 + √ 3) and (2 - √ 3).

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  1. 10 August, 19:03
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    Polynomial of the two zeroes

    (x - (2+rt (3)) (x - (2-rt (3)) = x^2 - 4x + 1

    divide it

    (x^4 - 7x^3 + 9x^2 + 13x - 4) / (x^2 - 4x + 1)

    = x^2 - 3x - 4

    = (x-4) (x+1)

    x=-1, 4 ... the remaining zeroes
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