SOLUTION: Write a polynomial with the zeros given. Zeros : 1 , 2+i , 2-i Thanks in advance!

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Question 1178286: Write a polynomial with the zeros given.
Zeros : 1 , 2+i , 2-i
Thanks in advance!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
Zeros : 1 , 2%2Bi+, 2-i

using zero product rule we have
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-1%29%28x-%282%2Bi%29%29%28x-%282-i%29%29
f%28x%29=%28x-1%29%28x-2-i%29%28x-2%2Bi%29
f%28x%29=%28x-1%29%28x%5E2+-+4x+%2B+5%29
f%28x%29=x%5E3+-+5x%5E2+%2B+9x+-+5