I was given this question for my Algebra class and am really struggling to find the answer. The problem: Given that f(x) is a cubic function with zeros at -7 and 4 i +3 , find an equation for f(x) given that f(-5) = -2.
Thank you all!
2026-03-24 22:06:30.1774389990
Find Cubic Given Zeroes
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Hint: If $c$ is a zero of $f$, then it must have a factor that is:
$$(x-c)$$
Also realize that you're dealing with imaginary roots, and must consider both $3+4i$ and $3-4i$ (as I'd assume real polynomial coefficients). That leaves you with:
$$f(x) = (x+7)(x-(3+4i))(x-(3-4i)) \times C$$
And solve for $C$ such that $f(-5)=-2$.