Which of the following represents the zeros of f (x) = x3 - 3x2 - 2x + 6?

A: - 3, - square root of 2, - square root of 2

B: 3, - square root of 2, - square root of 2

C: - 3, square root of 2, square root of 2

D: 3, square root of 2, - square root of 2

Answer D

Step-by-step explanation:

x^2 - 2 can be rewritten as (x-sqrt (2) (x+sqrt (2)). Thus, in factored form, we have f (x) = (x-3) (x-sqrt (2) (x+sqrt (2). Set this equal to zero and solve for the three roots:

x-3=0 yields x = 3.

x-sqrt (2) = 0 yields x = sqrt (2), and

x+sqrt (2) = 0 yields x = - sqrt (2).

This matches Answer D.