Solving Quadratic Equations

After identifying a quadratic equation, most of the questions require us to solve them. Meaning, making x or the unknown of the equation as the subject. This post will discuss the necessary skills for students to be able to do that.

How To Solve Them?

The "solutions" to the Quadratic Equation are where it is equal to zero.

They are also called "roots", or sometimes "zeros"

There are usually 2 solutions (as shown in this graph) and there are a few different ways to find the solutions:

We can Factor the Quadratic (find what to multiply to make the Quadratic Equation)

Or we can Complete the Square

Or we can use the special Quadratic Formula:

Just plug in the values of a, b and c, and do the calculations.

We will look at this method in more detail now.

About the Quadratic Formula

Plus/Minus

First of all, what is that plus/minus thing that looks like ± ?

The ± means there are TWO answers:

x = [−b+√(b2− 4ac)] / 2a

x = [−b-√(b2− 4ac)] / 2a

Let's look at the following example

Solve 5x^2 + 6x + 1 = 0

Coefficients are:a = 5, b = 6, c = 1 Quadratic Formula: x = [−b ± √(b2 − 4ac)] / 2a Put in a, b and c: x = [−6 ± √(62 − 4×5×1)] / 2×5

Solve: x = [−6 ± √(36 − 20)] / 10 x = [−6 ± √(16)] / 10 x = [−6 ± 4] / 10 x = −0.2 or −1