Posted by **ladybug** on Friday, November 23, 2012 at 2:59pm.

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!! -
**Reiny**, Friday, November 23, 2012 at 5:34pm
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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