Question

Which of the following is the complete list of roots for the polynomial function f (x) = (x squared + 6 x + 8) (x squared + 6 x + 13)?
–3 + 2i, –3 – 2i
–2, –4
–2, –4, –3 + 2i, –3 – 2i
–2, –4, –3 + 2i, 3 + 2i

Answer 1

Factor each quadratic:
x^2 + 6x + 8 = (x + 2)(x + 4) → roots -2, -4.
x^2 + 6x + 13 has discriminant 36 − 52 = −16, so roots (-6 ± 4i)/2 = -3 ± 2i.

Complete list: -2, -4, -3 + 2i, -3 − 2i.