SOLUTION: find the nth degree polynomial function with real coefficients satisfying the given conditions. n=3; -1 and -2 + 3i are zeros; leading coefficient is 1

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Question 762784: find the nth degree polynomial function with real coefficients satisfying the given conditions.
n=3; -1 and -2 + 3i are zeros; leading coefficient is 1


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Your THREE roots are -1, -2+3i, AND -2-3i.

Build your polynomial function using the polynomial factors according to the now known roots:

highlight%28%28x%2B1%29%28x-%282-3i%29%29%28x-%282%2B3i%29%29%29
Let us do something more convenient with the complex polynom factors.
%28x%2B1%29%28x-2%2B3i%29%28x-2-3i%29
%28x%2B1%29%28%28x-2%29%2B3i%29%28%28x-2%29-3i%29
You should notice what makes the difference of two squares.
%28x%2B1%29%28%28x-2%29%5E2+-+%283i%29%5E2%29
%28x%2B1%29%28x%5E2-4x%2B4%2B9%29
highlight%28%28x%2B1%29%28x%5E2-4x%2B13%29%29