Finding the Polynomial when given a complex root and an unknown root

Question

I have a problem here that is asking for a third degree polynomial. The roots that have been given to me are x=3i. Naturally I know that complex roots come in pairs so there also has to be x=-3i. There is an unknown root x=w. It also says f(1)=50 and the leading coefficient of f(x) is 1. How do I solve for w and get the polynomial? Thank you.

Answer 1

f(x) = (x - 3i)(x + 3i)(x - w)

f(x) = (x² + 9)(x - w)

f(x) = x² + 9x - wx² - 9w

f(1) = 50

50 = (1)² + 9(1) - w(1)² - 9w

50 = 10 - 10w

40 = -10w

-4 = w