Question

Assuming an equation with one side as a squared variable expression and the other side as a numeric expression, which of the following statements is correct?



(1 point)
Responses

Statement #1: If the numeric expression is zero, there are two solutions.
Statement #1: If the numeric expression is zero, there are two solutions.

Statement #2: If the numeric expression is zero, there is one solution.
Statement #2: If the numeric expression is zero, there is one solution.

Statement #3: If the numeric expression is zero, there are no solutions.

Answer 1

To analyze the statements regarding an equation with one side as a squared variable expression and the other side as a numeric expression:

We can represent the equation as \( x^2 = k \), where \( k \) is the numeric expression.

1. **If the numeric expression is zero** (i.e., \( k = 0 \)):
- The equation becomes \( x^2 = 0 \).
- The solution to this equation is \( x = 0 \).
- Therefore, there is **exactly one solution**.

Based on this analysis:

- **Statement #1**: Incorrect (there are not two solutions).
- **Statement #2**: Correct (there is one solution).
- **Statement #3**: Incorrect (there is a solution).

Thus, the correct response is:

**Statement #2: If the numeric expression is zero, there is one solution.**