Question

Which of the following is a polynomial with roots 2, 3i, and -3i?

A. f(x) = x^3 - 2x^2 + 6x - 9
B. f(x) = x^3 - 6x ^2 + 9x - 18
C. f(x) = x^3 - 6x^2 + 18x - 2
D. f(x) = x^3 + 2x^2 + 9x - 18

Answer 1

Since the roots are 2,3i, and -3i, you can write it as

(x-2)(x-3i)(x+3i)=(x-2)(x^2+9)=x^3-2x^2+9x-18.