ssuming 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. (1 po
Statement #1: If the numeric expression is zero, there are two solutions.
This statement is not necessarily correct. If the squared variable expression is also equal to zero, then there are indeed two solutions. However, if the squared variable expression is not zero, but the numeric expression is, then there is only one solution (which is when the squared variable expression equals zero).
Statement #2: If the numeric expression is zero, there is one solution.
This statement is partially correct. If the squared variable expression is also equal to zero, then there is only one solution. However, if the squared variable expression is not zero, there are no solutions.
Statement #3: If the numeric expression is zero, there are no solutions.
This statement is partially correct. If the squared variable expression is also equal to zero, then there are no solutions. However, if the squared variable expression is not zero, there is one solution.
In conclusion, statement #3 is correct. If the numeric expression is zero, there are no solutions.
Statement #1: If the numeric expression is zero, there are two solutions.
This statement is correct. If the numeric expression on the other side of the equation is zero, then there are two possible solutions for the squared variable expression. This is because when the squared variable expression equals zero, it can have two possible values: one positive and one negative.
To determine the number of solutions in an equation with a squared variable expression on one side and a numeric expression on the other side, we need to consider the discriminant of the equation. The discriminant tells us how many solutions there are based on its value. The discriminant is calculated as follows:
Discriminant (D) = b^2 - 4ac
where in the equation ax^2 + bx + c = 0, a, b, and c are the coefficients of the equation.
Now let's analyze each statement:
Statement #1: If the numeric expression is zero, there are two solutions.
This statement is incorrect because the numeric expression being zero does not guarantee that there will always be two solutions. It depends on the value of the discriminant. If the discriminant is positive, there are two distinct solutions. If the discriminant is zero, there is one repeated solution. If the discriminant is negative, there are no real solutions.
Statement #2: If the numeric expression is zero, there is one solution.
This statement is partially correct. If the numeric expression is zero, it means we have an equation with the squared variable expression equal to zero. In this case, there will be one solution, which is when the variable is also zero.
Statement #3: If the numeric expression is zero, there are no solutions.
This statement is incorrect because if the numeric expression is zero, it means we have an equation with the squared variable expression equal to zero. In this case, there will always be at least one solution, which is when the variable is also zero.
So, the correct statement is Statement #2: If the numeric expression is zero, there is one solution.