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use the given zero to find all the zeros of the function.

f(x) = x^3 + x^2 + 9x + 9 r = 3i

I do not understand this!!

  • Math -

    the zeros (roots) could be found without the given hint that one of the roots is 3i

    f(x) = x^3 + x^2 + 9x + 9
    = x^2(x+1) + 9(x+1)
    = (x^2+9)(x+1)

    for the zeros,
    x+1 = 0 or x = -1
    or
    x^2 + 9 = 0
    x^2 = -9
    x = ±3√-1
    = ±3i

    so the roots are ±3i, -1

    Using the given hint that 3i is a root, one property of irrational or complex roots is that they must come in "conjugate pairs" to end up with rational coefficients.

    so 2 factors would be (x-3i) and (x+3i)

    then (x+3i)(x-3i) = x^2 + 9

    Using long division, divide your original function by x^2 + 9 to get the other factor of x+1

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