SOLUTION: Find a fourth degree polynomial function f(x) with real coefficients that has i and 3i as zeros such that f(-1)=20

Question 1072882: Find a fourth degree polynomial function f(x) with real coefficients that has i and 3i as zeros such that f(-1)=20
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If a polynomial has real coefficients,
and a complex zero,
the conjugate complex number should also be a zero.
In other words, if is a zero, so is .
In this case, and are also zeros.
With those four different zeros, a fourth degree polynomial must have the factored form
for some real non-zero number .
Simplifying,

-->-->-->--> .
So or multiplying the factors .
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