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?

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

(1 point)

Answer 1

When you have an equation where one side is a squared variable expression (like \( x^2 \)) and the other side is a numeric expression, you can analyze the situation when the numeric expression is zero.

Let's represent the equation as \( x^2 = k \), where \( k \) is the numeric expression. If \( k = 0 \), the equation becomes:

\[
x^2 = 0
\]

The solution to this equation is found by taking the square root of both sides:

\[
x = 0
\]

In this case, there is only one solution (specifically, \( x = 0 \)). Therefore:

- Statement #1 is incorrect (there are not two solutions).
- Statement #2 is correct (there is one solution).
- Statement #3 is incorrect (there are solutions; specifically, there is one solution).

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