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20 October, 14:13

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

A. x3 - 2x2 + 2x - 1

B. 3x3 + 2x2 - 5x + 3

C. x3 + 2x2 - x - 1

D. x3 + x2 - 4x + 6

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  1. 20 October, 17:18
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    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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