Answer:
4 - i, 4 + i, 2.
Step-by-step explanation:
Complex zeros exist as conjugate pairs so another zero is 4 + i.
So one factor of f(x) is
(x - (4 + i))(x - (4 - i))
= (x - 4 - i)(x - 4 + i)
= x^2 - 4x + ix - 4x + 16 - 4i - ix + 4i - i^2
= x^2 - 8x + 16 - (-1)
= x^2 - 8x + 17
Dividing:
x^2 - 8x + 17 ) x3 - 10x2 + 33x - 34( x - 2
x3 - 8x^2 + 17x
-2x^2 + 16x - 34
-2x^2 + 16x - 34
So the third root is 2:
x - 2 = 0
x = 2.
