Question

Using the given zero, find all other zeros of f(x) -2i is a zero of f(x) = x^4 - 32x^2 - 144

@agent0smith

Answer 1

Recall that complex zeros always come in conjugate pairs.
So if,
\[\Large\sf x=-2\mathcal i\]is a zero,
then so is,\[\Large\sf x=2\mathcal i\]Which means this polynomial has factors of,\[\Large\sf (x-2\mathcal i)(x+2\mathcal i)\]

Answer 2

Let's multiply out the brackets,
after that we can do polynomial long division or synthetic division to simplify the polynomial.

Answer 3

So what do you get when you multiply out the two brackets? :o
Understand how to do that?

Answer 4

You can also factor this since it's basically a quadratic equation\[\large x^4 - 32x^2 - 144 = (x^2 +4) (x^2 -36)\]then you can use diff. of two squares on the 2nd set of brackets