SOLUTION: Find a polynomial with the given zeros. i,i,2

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Question 167738: Find a polynomial with the given zeros.
i,i,2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since i, i, and 2 are given zeros this means that:


x=i, x=i, and x=2


Get all terms to the left side in each case


x-i=0, x-i=0, and x-2=0


Now use the zero product property in reverse to join the factors.


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


FOIL %28x-i%29%28x-i%29 to get x%5E2-2xi-1


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


%28x-2%29%28x%5E2-2xi-1%29=0 Rearrange the terms.



x%28x%5E2-2xi-1%29-2%28x%5E2-2xi-1%29=0 Expand


x%5E3-2x%5E2i-x-2x%5E2%2B4xi%2B2=0 Distribute


x%5E3%2B%28-2x%5E2i-2x%5E2%29%2B%28-x%2B4xi%29%2B2=0 Group like terms.


x%5E3-x%5E2%282i%2B2%29-x%281-4i%29%2B2=0 Factor out the GCF from each group


x%5E3-%282i%2B2%29x%5E2-%281-4i%29x%2B2=0 Rearrange the terms.


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Answer:

So the polynomial with roots of i, i, and 2 is

y=x%5E3-%282i%2B2%29x%5E2-%281-4i%29x%2B2