Question

Find a fourth degree polynomial function with real coefficients that has 2, -2 and -3i as zeros

Answer 1

Hint: a fourth degree polynomial function \(f(x)\) with roots \(a\), \(b\), \(c\), and \(d\) has the following form.\[f(x)=(x-a)(x-b)(x-c)(x-d)\]

Answer 2

in addition, complex roots always come in conjugate pairs... so if -3i is a zero, then so is 3i.

Answer 3

Yes, that is if you want your polynomial to be real.

Answer 4

thanks!!