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26 March, 09:18

Find the roots for f (x) = x4 + 21x2 - 100.

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  1. 26 March, 09:56
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    We will use the substitution:

    t = x²;

    t² + 21 x - 100 = 0

    t² + 25 t - 4 t - 100 = 0

    t (t + 25) - 4 (t + 25) = 0

    (t + 25) (t - 4) = 0

    t 1 = - 25, t 2 = 4

    x = √t

    Answer:

    The roots are:

    x 1 = 5 i

    x 2 = - 5 i

    x 3 = - 2

    x 4 = 2
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