# Quadratic Equation Tutorial

## Quadratic Equation Tutorial

##### Quadratic Equation Definition:

A quadratic equation is a polynomial equation of the second degree. The general form is ax^{2}+bx+c=0, where a ≠0.

#### Quadratic Equation Formula :

ax^{2} + bx + c = 0,
###### where

a = coefficient of x^{2}
b = coefficient of x and
c = constant.
#### Quadratic Equation solving formula:

x = (- b ± √ b^{2} - 4 * a * c) / 2 * a
##### Example 1 :

Calculate the roots(x1, x2) of the quadratic equation,
x^{2} + 2x - 8 = 0.

###### Step 1:

From the above equation, the value of a = 1, b = 2 and c = - 8.

###### Step 2:

To Find X:
Substitute the values in the formula below
x = (- b ±√ b^{2} - 4 * a * c) / 2 * a

###### Step 3:

We get the roots,
x = (- 2 ±√ 2^{2} - 4 * 1 * - 8) / 2 * 1
x = - 4 and x = 2
which means x1 = - 4 and x2 = 2.

##### Example 2 :

Calculate the roots(x1, x2) of the quadratic equation, x^{2} - 10x + 25 = 0

###### Step 1:

From the above equation, the value of a = 1, b = - 10 and c = 25.

###### Step 2:

To Find X:
Substitute the values in the formula below
x = (- b ±√ b^{2} - 4 * a * c) / 2 * a

###### Step 3:

We get the roots,
x = (- 2 ±√ 2^{2} - 4 * 1 * - 8) / 2 * 1
x = 5 and x = 5
which means x1 = 5 and x2 = 5.
Here x = 5 is called the double root.
A quadratic will have a double root if the quadratic is a perfect square trinomial.

This tutorial will help you dynamically to find the roots of a quadratic equation.