find a polynomial of:?

Question

with degree of 4, that has zeros -2, 2, 3i

Answer 1

If 3i is a root, then - 3i must be also.

y = (x+2)(x-2)(x-3i)(x+3i)

Mult together is you need to.

y = (x^2 - 4)(x^2 + 9)

y = x^4 + 5x^2 - 36

Answer 2

Let's assume your polynomial has real coefficients.
Then -3i is its 4th root, because if a+bi is a root,
so is a-bi.
So the answer is
P(x) = (x+2)(x-2)(x+3i)(x-3i) = (x²-4)(x²+9) = x^4 + 5x² - 36.