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)

Question

Responses

If the numeric expression is zero, there is one solution.
If the numeric expression is zero, there is one solution.

If the numeric expression is zero, there are two solutions.

If the numeric expression is zero, there are two solutions.

If the numeric expression is zero, there are no solutions.

Answer 1

When an equation involves a squared variable expression set equal to a numeric expression, the analysis of solutions depends on the value of the numeric expression.

1. If the numeric expression is zero (for example, if the equation is \( x^2 = 0 \)), then there is indeed one solution, which is \( x = 0 \).

2. If the numeric expression is a positive number (for instance, \( x^2 = 4 \)), there will be two solutions (e.g., \( x = 2 \) and \( x = -2 \)).

3. If the numeric expression is negative (e.g., \( x^2 = -1 \)), there are no real solutions since a square cannot equal a negative number.

Given these points, the correct statement in the context of the provided options is:

If the numeric expression is zero, there is one solution.