*Sometimes, we will need to do some algebra to get the equation into standard form before we can use the Quadratic Formula.*

*Sometimes, we will need to do some algebra to get the equation into standard form before we can use the Quadratic Formula.*

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.

This quantity is called the When the discriminant is positive the quadratic equation has two solutions.

When the discriminant is zero the quadratic equation has one solution.

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, .

So factoring out −2 will result in the common factor of (r – 3).

If we had gotten (−r 3) as a factor, then when setting that factor equal to zero and solving for r we would have gotten: There are many applications for quadratic equations.

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.

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