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.

Answer 1

Let's examine the implications of the equation in question, which has a squared variable expression on one side and a numeric expression (assumed to be zero for analysis) on the other side.

Assuming the equation takes the form \( ax^2 + bx + c = 0 \):

1. If we rewrite this as \( x^2 = 0 \), the expression on the left side is a squared term.

2. When the numeric expression is zero, we have \( x^2 = 0 \).

Now, let's analyze what happens:

- The equation \( x^2 = 0 \) can be solved by taking the square root of both sides, yielding \( x = 0 \).
- This means that there is **exactly one solution**: \( x = 0 \).

Based on this analysis:

- **Statement #1**: "If the numeric expression is zero, there are two solutions." **(Incorrect)**.
- **Statement #2**: "If the numeric expression is zero, there is one solution." **(Correct)**.
- **Statement #3**: "If the numeric expression is zero, there are no solutions." **(Incorrect)**.

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