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.
Statement #2: If the numeric expression is zero, there is one solution.
Statement #2: If the numeric expression is zero, there is one solution.
To determine which statement is correct, we need to understand the nature of the equation with one side as a squared variable expression and the other side as a numeric expression.
Let's consider a general equation in the form of "ax^2 + bx + c = 0," where a, b, and c are coefficients and x is the variable. In this case, the squared variable expression is ax^2 + bx + c.
To solve this equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Now, let's analyze each statement:
Statement #1: If the numeric expression is zero, there are two solutions.
If the numeric expression is zero (e.g., ax^2 + bx = 0), then we have ax^2 + bx = 0, which can be factored as x(ax + b) = 0. By the zero product property, either x = 0 or ax + b = 0. Therefore, there are two solutions when the numeric expression is zero.
Statement #2: If the numeric expression is zero, there is one solution.
Since we have already established that when the numeric expression is zero, there are two solutions, Statement #2 is incorrect.
Statement #3: If the numeric expression is zero, there are no solutions.
Again, we already identified that when the numeric expression is zero, there are two solutions. Statement #3 is also incorrect.
Therefore, the correct statement is Statement #1: If the numeric expression is zero, there are two solutions.