SOLUTION: Find a 3^10 degree polynomial function with real coefficients; given zeros are 2 and 2i, and f(1) = 10

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Question 357714: Find a 3^10 degree polynomial function with real coefficients; given zeros are 2 and 2i, and f(1) = 10
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since 2i is a root, then -2i is also a root.
f%28x%29=a%28x-2%29%28x%2B2i%29%28x-2i%29
f%28x%29=a%28x-2%29%28x%5E2%2B4%29
f%281%29=a%281-2%29%281%2B4%29=10
a%28-1%29%285%29=10
a=-2
.
.
f%28x%29=-2%28x-2%29%28x%5E2%2B4%29
f%28x%29=-2%28x%5E3%2B4x-2x%5E2-8%29
highlight%28f%28x%29=-2x%5E3%2B4x%5E2-8x%2B16%29