SOLUTION: find a third-degree polynomial equation with rational coefficients that has 1 and 3i as roots.

Question 571790: find a third-degree polynomial equation with rational coefficients that has 1 and 3i as roots.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If the coefficients are rational numbers, irrational roots have to appear in conjugate pairs, so -3i must also be a root.
A polynomial of degree 3, with 1, 3i, and -3i as roots has to be equal to
with some rational non-zero number , and all polynomials of such form are of degree 3, and have 1, 3i, and -3i as roots.
So there are infinite such polynomials for the answer, but the simplest, with is

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