Question

Which value is a zero of the function f(x) = x³ − 5x² − 8x + 12?

1 )-1
2)2
3)6
4) 12

Answer 1

Only 6 match your answer choices.

Explanation:

Solve for x:

x^3 - 5 x^2 - 8 x + 12 = 0

The left-hand side factors into a product with three terms:

(x - 6) (x - 1) (x + 2) = 0

Split into three equations:

x - 6 = 0 or x - 1 = 0 or x + 2 = 0

Add 6 to both sides:

x = 6 or x - 1 = 0 or x + 2 = 0

Add 1 to both sides:

x = 6 or x = 1 or x + 2 = 0

Subtract 2 from both sides:

Answer: x = 6 or x = 1 or x = -2