- A-Level Maths

# Quadratic & Simultaneous Equations and Inequalities

The standard format of a quadratic expression is **ax² + bx + c**

There are three ways of solving quadratic equations:

### Factorising

Factorise a quadratic in the form *ax² + bx + c = 0*, and set each bracket to equal 0 to find the values of x (the roots).

### The Quadratic Equation

The** (b² - 4ac)** inside the square root is known as the **discriminant**, and is used to show how many roots a quadratic has:

**b² - 4ac > 0:**The quadratic has**two distinct roots****b² - 4ac = 0:**The quadratic has**one repeated root****b² - 4ac < 0:**The quadratic has**no real roots**

### Completing the Square

More commonly, quadratics are in their standard form. In this case, this version is used: