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.
The correct statement is Statement #2: If the numeric expression is zero, there is one solution.
To determine which statement is correct, we need to understand the general behavior of equations with squared variable expressions and numeric expressions.
In general, an equation with a squared variable expression can have zero, one, or two solutions. This is because a squared variable can have two possible values, namely the positive and negative square roots of a given number.
Now let's analyze each statement:
Statement #1: If the numeric expression is zero, there are two solutions.
If the numeric expression is zero, it means the equation simplifies to a squared variable expression equal to zero. In this case, there would be two solutions because a squared variable equal to zero has both a positive and negative solution. So, statement #1 is generally correct.
Statement #2: If the numeric expression is zero, there is one solution.
If the numeric expression is zero, it would mean that the equation simplifies to a squared variable expression equal to zero. As mentioned earlier, a squared variable equal to zero has two solutions (positive and negative). So, statement #2 is not correct.
Statement #3: If the numeric expression is zero, there are no solutions.
If the numeric expression is zero, it means the equation simplifies to a squared variable expression equal to zero. As mentioned earlier, a squared variable equal to zero has two solutions (positive and negative). So, statement #3 is not correct.
Based on these explanations, the correct statement is: Statement #1: If the numeric expression is zero, there are two solutions.