# Problem Solving Using Quadratic Equations

When you use the Principle of Zero Products to solve a quadratic equation, you need to make sure that the equation is equal to zero.For example, 12x 10m as 2m(m 5) and then set the factors equal to 0.

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However, the original equation is not equal to 0, it’s equal to 48.

To use the Zero Product Property, one side must be 0.

The result gives the solution(s) to the quadratic equation.

When we solved quadratic equations by using the Square Root Property, we sometimes got answers that had radicals.

We cannot take the square root of a negative number.

So, when we substitute , , and into the Quadratic Formula, if the quantity inside the radical is negative, the quadratic equation has no real solution. The quadratic equations we have solved so far in this section were all written in standard form, .

The correct answer is m = You can find the solutions, or roots, of quadratic equations by setting one side equal to zero, factoring the polynomial, and then applying the Zero Product Property.

The Principle of Zero Products states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0.

This gave us an equivalent equation—without fractions—to solve.

We can use the same strategy with quadratic equations. We know from the Zero Products Principle that this equation has only one solution: .

## Comments Problem Solving Using Quadratic Equations

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