SOLUTION: Find a polynomial with zeros: -2, 2-i; f(x)=

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Question 949390: Find a polynomial with zeros: -2, 2-i;
f(x)=
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a polynomial with zeros x%5B1%5D=-2 and +x%5B2%5D=2-i must have zero +x%5B3%5D=2%2Bi because complex zeros always come in a pairs
then we have:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-%28-2%29%29%28x-%282-i%29%29%28x-%282%2Bi%29%29
f%28x%29=%28x%2B2%29%28x-2%2Bi%29%28x-2-i%29
f%28x%29=%28x%2B2%29%28x%5E2-2x-xi-2x%2B4%2B2i%2Bxi-2i-i%5E2%29

f%28x%29=%28x%2B2%29%28x%5E2-4x%2B4%2B1%29
f%28x%29=%28x%2B2%29%28x%5E2-4x%2B5%29
f%28x%29=x%5E3-4x%5E2%2B5x%2B2x%5E2-8x%2B10
f%28x%29=x%5E3-2x%5E2-3x%2B10-> your answer

+graph%28+600%2C600%2C+-10%2C+10%2C+-10%2C+15%2C+x%5E3-2x%5E2-3x%2B10%29+