Question

Recognize which of the following statements is true.(1 point)
Responses

When k
is negative, x2=k
has one solution, which is negative.
When k is negative, x squared equals k has one solution, which is negative.

When k
is positive, x2=k
has one solution, which is positive.
When k is positive, x squared equals k has one solution, which is positive.

When k
is negative, x3=k
has one solution, which is negative.
When k is negative, x cubed equals k has one solution, which is negative.

When k
is positive, x3=k
has one positive solution and one negative solution.

Answer 1

Only the third statement is true.

- x^2 = k: if k < 0 there are no real solutions; if k > 0 there are two real solutions ±√k.
- x^3 = k: for k < 0 there is exactly one real solution, x = ∛k (which is negative); for k > 0 there is exactly one real solution, x = ∛k (positive).