Question

Fully factored form: f(x) = (x − 3)(x + 3)[x − (2 − i)][x − (2 + i)] The function has ____ real roots and ____ imaginary roots.

Answer 1

2 real roots and 2 imaginary roots

f(x) = (x - 3)(x + 3 )(x-2 + i)(x - 2 - i)

(x - 3) and (x + 3) give real roots x = ± 3

(x - 2 + i)(x - 2 - i) give 2 imaginary roots x = 2 ± i