### Roots of a Quadratic Equation

What do we mean by the roots of a quadratic equation?

Example 1

We say that 2 and 1 are roots of the equation. The equation has 2 real and distinct roots

In graphical form, the roots of the equation are represented as the intersection of the curve with the x axis.

Example 2

In this case there is only 1 solution. We say that the equation has only 2 real and equal roots

Graphically it can be represented as

Notice that there is only 1 intersection point between the curve and the x axis

Example 3

Lastly we are going to look at an example where the curve does not intersect the x axis

Consider the equation:

The equation cannot be factorized. It cannot be solved using the quadratic formula.

Graphically it is represented as

It turns out that we can predict the number of roots that an equation has by looking at the discriminant

Recall the quadratic formula

Example 1

We say that 2 and 1 are roots of the equation. The equation has 2 real and distinct roots

In graphical form, the roots of the equation are represented as the intersection of the curve with the x axis.

Example 2

In this case there is only 1 solution. We say that the equation has only 2 real and equal roots

Graphically it can be represented as

Notice that there is only 1 intersection point between the curve and the x axis

Example 3

Lastly we are going to look at an example where the curve does not intersect the x axis

Consider the equation:

The equation cannot be factorized. It cannot be solved using the quadratic formula.

Graphically it is represented as

It turns out that we can predict the number of roots that an equation has by looking at the discriminant

Recall the quadratic formula