Which of the following is a polynomial with degree 3 and zeros –3 and 1 + i?

1 answer:

8 0

Take the complex zero 1+i. There must be another zero 1-i to balance it, so we have the factors (x-1-i)(x-1+i)=x²-2x+1+1=x²-2x+2.
So the polynomial is (x+3)(x²-2x+2)=x³-2x²+2x+3x²-6x+6=x³+x²-4x+6, option D.

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