SOLUTION: what is the simplest polynomial equation that has roots 1-2i and -3?

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Question 121413: what is the simplest polynomial equation that has roots 1-2i and -3?
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
In polynomial function equations, complex roots always occur in conjugate pairs.
So if (1-2i) is a solution, so is (1+2i).
The simplest form, g(x), would then be,
g%28x%29=%28x-%281-2i%29%29%28x-%281%2B2i%29%29%28x-%28-3%29%29
g%28x%29=%28x-1%2B2i%29%28x-1-2i%29%28x%2B3%29
g%28x%29=%28x%5E2-2x%2B5%29%28x%2B3%29
g%28x%29=%28x%5E3-2x%5E2%2B5x%29%2B%283x%5E2-6x%2B15%29
g%28x%29=x%5E3%2Bx%5E2-x%2B15