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use the given zero

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Use the given zero to find the remaining zeros of the function.
f(x)=x^3-2x^2+9x-18;zero;3i
Enter the remaining zeros of f
=

  • use the given zero -

    The function is actually quite easy to factor using grouping
    f(x_ = x^3 - 2x^2 + 9x - 18
    = x^2(x-2) + 9(x-2)
    = (x-2)(x^2+9)

    so x^2 + 9 = 0 ----> x = ± 3i
    and x-2 = 0 ---> x = 2

    the other way:
    since complex roots always come in conjugate pairs
    the other one had to be -3i
    and its corresponding factor would have been x^2 = 9
    dividing this into the f(x) function would have given us the other remaining factor of (x-2) for the third root of 2

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