SOLUTION: Form a polynomial F(x) with real coefficients having the given degree and zeros. Degree 4 ; Zeros: 2-2i; 4 Multiplicity 2 F(x)=a(?)

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Question 916425: Form a polynomial F(x) with real coefficients having the given degree and zeros.
Degree 4 ; Zeros: 2-2i; 4 Multiplicity 2
F(x)=a(?)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
F%28x%29=%28x-%282-2i%29%29%28x-%282%2B2i%29%29%28x-4%29%5E2, complex roots occur in conjugate pairs.

The two factors with the complex roots form a quadratic product which you find through just multiplication:
%28x-2%2B2i%29%28x-2-2i%29
%28%28x-2%29%2B2i%29%28%28x-2%29-2i%29
%28x-2%29%5E2-%284i%5E2%29
x%5E2-4x%2B4-%28-1%294x%5E2-4x%2B4%2B4
x%5E2-4x%2B8

Summarizing F:
highlight%28F%28x%29=%28x%5E2-4x%2B8%29%28x-4%29%5E2%29
Still in factored form. You can multiply and simplify to arrange in general form for a polynomial of sum of terms.