SOLUTION: Use the given zero to find all the zeros of the function g(x)=x^3-7x^2-x+87 zero: 5+2i

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Question 418430: Use the given zero to find all the zeros of the function
g(x)=x^3-7x^2-x+87 zero: 5+2i
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
If 5 + 2i is a zero, then 5 - 2i must also be a zero. Let r be the third zero.
Then from algebra, the sum of the roots of the polynomial taken one at a time is equal to -%28-7%29%2F1+=+7, so that r + (5 + 2i) + (5 - 2i) = 7, or r + 10 = 7, or r = -3. Therefore the zeros of the polynomial are -3, 5 + 2i, and 5 - 2i.