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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

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Answer:

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.

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