SOLUTION: i have to find a 3rd degree polynomial equation with rational coefficient that has the given numbers as roots. 3+ i and negative 3

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Question 930160: i have to find a 3rd degree polynomial equation with rational coefficient that has the given numbers as roots.
3+ i and negative 3
Answer by josgarithmetic(39627) About Me  (Show Source):
You can put this solution on YOUR website!
Very routine question for polynomials.

3-i is also a root because complex roots occur as conjugate pairs.

highlight_green%28%28x-%283%2Bi%29%29%28x-%283-i%29%29%28x-%28-3%29%29=0%29, the start.
%28x-3-i%29%28x-3%2Bi%29%28x%2B3%29=0
%28%28x-3%29-i%29%28%28x-3%29%2Bi%29%28x%2B3%29=0
%28%28x-3%29%5E2-i%5E2%29%28x%2B3%29=0
%28%28x-3%29%5E2%2B1%29%28x%2B3%29=0
%28x%5E2-6x%2B9%2B1%29%28x%2B3%29=0
highlight%28%28x%5E2-6x%2B10%29%28x%2B3%29=0%29.
You can continue multiplying if needed.