SOLUTION: Write a third degree polynomial function y=P(x) with rational coefficients so that P(x)=0 has the given roots. 3, 6+i

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Question 819539: Write a third degree polynomial function y=P(x) with rational coefficients so that P(x)=0 has the given roots.
3, 6+i
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
There is one more root; include 6-i as one of them.

P%28x%29=0=%28x-3%29%28x-%286%2Bi%29%29%28x-%286-i%29%29
P%28x%29=%28x-3%29%28x-6-i%29%28x-6%2Bi%29
%28x-3%29%28%28x-6%29-i%29%28%28x-6%29%2Bi%29, recognize the difference of two squares for the result, and that i*i=-1,
%28x-3%29%28%28x-6%29%5E2%2B1%29
%28x-3%29%28x%5E2-12x%2B36%2B1%29
%28x-3%29%28x%5E2-12x%2B37%29
and you can finish the multiplication for the two polynomial factors.