Question

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

x3 - 4x2 + 4x - 16
x3 + 4x2 + 4x + 16
x3 + 2x2 + 4x + 8
x3 - 2x2 + 4x - 8

Answer 1

for complex roots
\[x = \pm2i\]
\[x^{2} = -4\]
\[x^{2}+4 = 0\]
this gives the factor for the 2 complex roots, now multiply by factor for real root
\[\rightarrow(x+2)(x^{2}+4) = x^{3}+2x^{2}+4x+8\]