A polynomial of degree 3, P(x) has leading coefficient 1, and has roots of 4 i and 8.

Answer 1

You did not ask a question, but I assume you want the expression for the polynomial. If you want it to have only real coefficients (a condition not stated in the problem), then the complex conjugate of any complex root must also be a root. Hence, the roots are

4i

-4i

8

If the leading coefficient is 1, then

p(x) = 1(x - 8)(x - 4i) [x - (-4i)]

p(x) = (x - 8)(x - 4i)(x + 4i)

You can expand to standard form if you wish.