Skip to Main Content
It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.

Math

Attribution

Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in October 2020. This work is licensed under a Creative Commons BY 4.0 International License.

The Quadratic Formula

 

Another method to solve a quadratic equation is using the quadratic formula. For a quadratic equation of the form:

                                                                                 

The quadratic formula is given by:
                                                                                   

 

The number of solutions of a quadratic equation depends on the radical term in the quadratic formula. There are three cases for the solutions of a quadratic equation:

 

Case 1) , the equation has two solutions.
Case 2) , the equation has one solution.
Case 3) , the equation has no real solutions.

 

Example: Solve  using the quadratic formula.
We identify the following coefficients:

We now have to substitute the above values into the quadratic formula and simplify:

 

Example: Solve  using the quadratic formula.
We identify the coefficients in the quadratic equation:

Using the quadratic formula we get:

 

Example: Solve  using the quadratic formula. 
We have the following coefficients:

now, we put the above values in the quadratic formula:

since there is a negative number under the square root, the equation has no real solutions.

 

 

Grande Prairie Campus
10726 - 106 Avenue
Grande Prairie, AB T8V 4C4
Phone: 1-780-539-2939
Email: library@nwpolytech.ca
Fairview Campus
11235-98 Avenue
Fairview,AB T0H 1L0
Phone: 1-780-835-6750
Email: fvlibrary@nwpolytech.ca
We acknowledge the Indigenous people and ancestors whose land we are on.