Question

Write a polynomial of the smallest degree with roots 4i and -4i.

Answer 1

If you have a polynomial with roots r1, r2, ... rn, it can be written in factored form as
(X-r1)(x-r2)...(x-rn)

Answer 2

ok, but I don't understand how that relates to the roots 4i and -4i...

Answer 3

Well, 4i is one root, so

(x-4i) is one factor

Can you tell me the other?

Answer 4

(x+4i) is the other factor

So (x-4i)(x+4i) is the polynomial with those roots, but you probably need to multiply it out to get the answer expected. Don't forget that i*i=-1