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.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)