Posted by ladybug on .
information is given about a polynomial f(x)whose coefficients are real numbers. Find the remaining zeros of f.
degree:5, zeros: 6, 6i
please help and show all work.

college algebraneed help please!! 
Reiny,
From the given zeros, factors would be
(x+6) , (x6i) and (x6 + 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