Question

The equation: x3=−8
will have how many solutions for x ?(1 point)

One solution: x = -2 since (−2)3
= -8

One solution: x = - 83
since the inverse operation is to divide by 3.

Two solutions: x = - 83
and x = 83
since x 3
equations always have 2 solutions

Two solutions: x = 8 and x = -8 since 23
= 8 and (−2)3
= -8

Answer 1

Correct choice: One solution: x = −2.

Reason: x^3 = −8 ⇒ x = cube root of −8 = −2. Over the real numbers the cubic function is one-to-one, so there is exactly one real solution, x = −2. (If complex solutions are allowed there are three cube roots: −2, 1 + i√3, and 1 − i√3.)