Question

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

Answer 1

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.