## What are the roots of the quadratic function?

The **roots** (or zeros) of the quadratic function are the points where the graph intercepts the x-axis. To calculate the **roots**, it is necessary to write the function equal to zero, obtaining a second degree polynomial equation. There are many methods to solve second degree polynomial equations but, the most used one is the application of the Bhaskara formula, also known as the quadratic formula:

So, using the formula to solve the equation **ax² + bx + c = 0**, we get:

The graph of a quadratic function is a line known as a **parabola** and it intercepts the x-axis in, up to, two points:

- if b
^{2}-4ac > 0, the equation has two distinct real**roots**and the**parabola**intercepts the x-axis in two different points (x1 ≠ x2); - if b
^{2}-4ac = 0, the equation has two equal real**roots**and the**parabola**is tangent to the x-axis (x1 = x2); - if b
^{2}-4ac < 0, the equation has no real**roots**and the**parabola**does not intercept the x-axis;

#### Example of how to calculate the roots of a quadratic equation

Find the zeros of the function **f(x) = x ^{2} – 5x + 6**.

Solution:

If:

a = 1

b = – 5

c = 6

x^{2} – 5x + 6 = 0

Replacing in the formula:

The value of b^{2}-4ac > 0 , so there are two real distinct **roots**, which are 2 and 3, meaning that the function intercepts the x-axis at the points (2, 0) and (3, 0).