SOLUTION: Find a third degree polynomial that has x=1 as its only real zero and this zero has: A. Multiplicity one(1) B. Multiplicity three(3)

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Question 734414: Find a third degree polynomial that has x=1 as its only real zero and this zero has:
A. Multiplicity one(1)
B. Multiplicity three(3)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Third Degree Polynomial:
%28x-a%29%28x-b%29%28x-c%29

A real zero is x=1:
%28x-1%29%28x-b%29%28x-c%29

x=1 is the only real zero, and multiplicity is 1:
%28x-1%29%28x-z%5B1%5D%29%28x-z%5B2%5D%29,
where we want two complex numbers as conjugate pairs. This part is open-ended. For convenience we could pick 1-i and 1+i.
%28x-1%29%28x-%281-i%29%29%28x-%281%2Bi%29%29
%28x-1%29%28x%5E2-%281-i%29x-%281%2Bi%29x%2B%281-i%29%281%2Bi%29%29
%28x-1%29%28x%5E2-x%2Bix-x-ix%2B1%2B1%29
highlight%28%28x-1%29%28x%5E2-2x%2B2%29%29