To evaluate the statements regarding an equation with one side as a squared variable expression and the other side as a numeric expression, let's consider a general equation of the form:
\[ ax^2 = c \]
where \( a \) is a non-zero constant, \( x \) is the variable, and \( c \) is the numeric expression.
Now, if \( c = 0 \), the equation becomes:
\[ ax^2 = 0 \]
To find the solutions, we can solve for \( x \):
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Divide both sides by \( a \) (since \( a \neq 0 \)): \[ x^2 = 0 \]
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Taking the square root of both sides gives: \[ x = 0 \]
In this case, there is exactly one solution, which is \( x = 0 \).
Now let's evaluate the statements:
- 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 is correct.