SOLUTION: Form a polynomial f(x) with real coefficients Degree: 4; Zeros; -1,2 and 1, -2i

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Question 732260: Form a polynomial f(x) with real coefficients
Degree: 4; Zeros; -1,2 and 1, -2i
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Form a polynomial f%28x%29 with real coefficients
Degree: 4; Zeros; -1,2 and 1, -2i
use the zero product rule ...f%28x%29=0
%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29=0...plug in x%5B1%5D=-1,x%5B2%5D=2, x%5B3%5D=1, and x%5B4%5D=-2i

%28x-%28-1%29%29%28x-2%29%28x-1%29%28x-%28-2i%29%29=0

%28x%2B1%29%28x-2%29%28x-1%29%28x%2B2i%29=0

%28x%5E2-2x%2Bx-2%29%28x%5E2%2B2xi-1x-2i%29=0

%28x%5E2-x-2%29%28x%5E2%2B2xi-2i-1x%29=0

%28x%5E2-x-2%29%28x%5E2%2B2i%28x-1%29-1x%29=0

x%5E4-%282-2i%29x%5E3-%281%2B4i%29x%5E2%2B%282-2i%29x%2B4i=0
or
f%28x%29=x%5E4-%282-2i%29x%5E3-%281%2B4i%29x%5E2%2B%282-2i%29x%2B4i