## Equation and its roots

An equation is a mathematical expression that contains an unknown quantity that we are trying to find.

For example, consider the equation **x** – 3 = 7. Here,** x** is the unknown quantity.

The root of the equation is a number that, when substituted for the unknown, turns the equation into a correct equality.

Suppose, if x = 2, then substituting this value into the equation, we get 2 – 3 = 7. It turns out, -1 = 7, which is an incorrect equality. Therefore, x = 2 is not a root of the equation.

But if x = 10, then substituting this value into the equation, we get 10 – 3 = 7. It turns out, 7 = 7, which is a correct equality. Therefore, x = 10 is a root of the equation.

To solve an equation means to find all its roots or to prove that they do not exist.

## Quadratic equation

A quadratic equation is an equation of the form **a**x² +** b**x + **c** = 0, where** a** is the coefficient at x² (it should not be zero), **b** is the coefficient at x, **c** is the free term.

To better remember how the coefficients are located, let’s try to determine them on examples.

- Equation: 2x² – 5x + 3 = 0

Coefficients:

a = 2

b = -5

c = 3 - Equation: -3x² + 4x – 2 = 0

Coefficients:

a = -3

b = 4

c = -2 - Equation: 6x² + 7x – 1 = 0

Coefficients:

a = 6

b = 7

c = -1

Now that you know how to determine the coefficients in a quadratic equation, you are ready for more complex tasks!