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