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college algebra--need help please!!

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information is given about a polynomial f(x)whose coefficients are real numbers. Find the remaining zeros of f.
degree:5, zeros: -6, 6-i

please help and show all work.

  • college algebra--need help please!! -

    From the given zeros, factors would be
    (x+6) , (x-6-i) and (x-6 + i)

    the complex factors simplify to x^2 -12x +37

    (complex numbers always appear in conjugate pair form)

    but that would only produce a cubic, so there has to be multiplicity of the above zeros.

    two options :

    f(x) = (x+6)^3 (x^2 - 12x + 37)
    or
    f(x) = (x+6)(x^2 - 12x + 37)^2

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