SOLUTION: write polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros 2, i, -i

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Question 848747: write polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros
2, i, -i
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Degree three, because you want exactly those three given roots. I will do this only part-way:

The binomial factors of f will be %28x-2%29%28x-i%29%28x-%28-i%29%29. Multiply the two imaginary factors first:
%28x-i%29%28+x-%28-1%29%29
%28x-i%29%28x%2Bi%29
x%5E2-i%5E2
x%5E2-%28-1%29
x%5E2%2B1
-
So revise the function expression as %28x-2%29%28x%5E2%2B1%29
... and you can finish the rest.