SOLUTION: Find a polynomial equation of degree 3 with integer coefficients that has x=10, 2i, -2i as its solutions

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Question 759161: Find a polynomial equation of degree 3 with integer coefficients that has x=10, 2i, -2i as its solutions
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Each of the roots gives you a binomial factor which composes the function. The simplest function for your given roots is
f%28x%29=%28x-10%29%28x-%282i%29%29%28x-%28-2i%29%29
Simply do the multiplications if you want general form:

%28x-2i%29%28x%2B2i%29=x%5E2-%284i%5E2%29=x%5E2%2B4, taken care of only the complex roots.

%28x-10%29%28x%5E2%2B4%29=x%5E3-10x%5E2%2B4x-40, included the other root.

highlight%28f%28x%29=x%5E3-10x%5E2%2B4x-40%29