find a polynomial function of degree 3 with 1+2i, 1-2i, -1 as zeros

find a polynomial function of degree 3 with 1+2i, 1-2i, -1 as zeros
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Take the complementary zeroes and multiply the factors: (x-1-2i)(x-1+2i)=x^2-2x+5. Finally multiply by the real zero as a factor: (x+1)(x^2-2x+5)=x^3-x^2+3x+5. The general polynomial is f(x)=a(x^3-x^2+3x+5) where a is a constant.

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