SOLUTION: Write a third degree polynomial function y = P(x) with rational coefficients so that P(x) = 0 has roots -2 and 6 + i

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Question 1131018: Write a third degree polynomial function y = P(x) with rational coefficients so that P(x) = 0 has roots -2 and 6 + i
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This and so many like it have been done already.

y=p(x)
zeros are v, and a+i.

Another zero is a-i.

p%28x%29=%28x-v%29%28x-%28a-i%29%29%28x-%28a%2Bi%29%29
%28x-v%29%28x-a%2Bi%29%28x-a-i%29
%28x-v%29%28%28x-a%29%2Bi%29%28%28x-a%29-i%29
%28x-v%29%28%28x-a%29%5E2-i%5E2%29
%28x-v%29%28%28x-a%29%5E2%2B1%29
highlight%28%28x-v%29%28x%5E2-2ax%2Ba%5E2%2B1%29%29, and you could multiply further to simplify .