college algebra--need help please!!
posted by ladybug .
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.
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)
f(x) = (x+6)(x^2 - 12x + 37)^2