SOLUTION: n=3 2 and 2i are zeros f(1)=-5 How do I solve this?

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Question 920869: n=3 2 and 2i are zeros f(1)=-5
How do I solve this?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
n=3+ ...........degree of the function
x%5B1%5D=2 and
x%5B2%5D=2i are zeros=> if complex number 2i is zero, then x%5B3%5D=-2i is zero too; they always come in pairs
f%281%29=-5
you can use zero product theorem to find equation:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-2%29%28x-2i%29%28x-%28-2i%29%29
f%28x%29=%28x-2%29%28x-2i%29%28x%2B2i%29
f%28x%29=%28x-2%29%28x%5E2-%282i%29%5E2%29
f%28x%29=%28x-2%29%28x%5E2-4%28i%29%5E2%29
f%28x%29=%28x-2%29%28x%5E2-4%28-1%29%29
f%28x%29=%28x-2%29%28x%5E2%2B4%29
f%28x%29=x%5E3%2B4x%5E2-2x%5E2-8
f%28x%29=x%5E3%2B2x%5E2-8
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3%2B2x%5E2-8%29+
check:f%281%29=-5
f%281%29=1%5E3%2B2%2A1%5E2-8
f%281%29=1%2B2-8
f%281%29=3-8
f%281%29=-5 ...this verifies our solution for f%28x%29