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24 April, 15:09

Find all of the zeros of the function f (x) = x^3-17x^2+81x-65

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  1. 24 April, 15:22
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    A graph shows the function can be factored as

    f (x) = (x - 1) ((x-8) ² + 1)

    There is one real root and there are two complex roots. The latter can be found from the vertex form factor:

    (x - 8) ² + 1 = 0

    (x - 8) ² = - 1

    x - 8 = ±√ (-1) = ±i

    x = 8 ± i

    The zeros of the function are {1, 8-i, 8+i}.
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