Identifying the Most Appropriate Method to Use to Solve a Quadratic Equation
Identifying the Most Appropriate Method to Use to Solve a Quadratic Equation
We have used four methods to solve quadratic equations:
- Factoring
- Square Root Property
- Completing the Square
- Quadratic Formula
You can solve any quadratic equation by using the Quadratic Formula, but that is not always the easiest method to use.
Identify the most appropriate method to solve a Quadratic Equation.
- Try Factoring first. If the quadratic factors easily, this method is very quick.
- Try the Square Root Property next. If the equation fits the form \(a{x}^{2}=k\) or \(a{\left(x-h\right)}^{2}=k\), it can easily be solved by using the Square Root Property.
- Use the Quadratic Formula. Any quadratic equation can be solved by using the Quadratic Formula.
What about the method of completing the square? Most people find that method cumbersome and prefer not to use it. We needed to include it in this tutorial because we completed the square in general to derive the Quadratic Formula. You will also use the process of completing the square in other areas of algebra.
Example
Identify the most appropriate method to use to solve each quadratic equation:
- \(5{z}^{2}=17\)
- \(4{x}^{2}-12x+9=0\)
- \(8{u}^{2}+6u=11\)
Solution
1. \(5{z}^{2}=17\)
Since the equation is in the \(a{x}^{2}=k\), the most appropriate method is to use the Square Root Property.
2. \(4{x}^{2}-12x+9=0\)
We recognize that the left side of the equation is a perfect square trinomial, and so Factoring will be the most appropriate method.
3. \(8{u}^{2}+6u=11\)
Put the equation in standard form. \(8{u}^{2}+6u-11=0\)
While our first thought may be to try Factoring, thinking about all the possibilities for trial and error leads us to choose the Quadratic Formula as the most appropriate method
Resources:
You can access these resources for additional instruction and practice with using the Quadratic Formula:
How to solve a quadratic equation in standard form using the Quadratic Formula (example)
Solving Quadratic Equations: Solving with the Quadratic Formula
This lesson is part of:
Introducing Quadratic Equations