Imaginary and Complex Solutions

Consider the following problem.

We can identify that

Now, substituting this into the Quadratic Formula:

Simplifying the expression under the radical gives:

Notice that there is a negative number under the square root symbol. If you are familiar with imaginary numbers, you know that the square root of a negative number is an imaginary number, which will cause the solutions to this example to also be imaginary or complex numbers.

In this lesson, we chose to expose you to this situation, but not to provide details on imaginary and complex solutions. We will add a lesson on this topic after we have introduced imaginary and complex numbers.