Year 10: Solve the quadratic equation by factorisation

This cheat sheet will guide you through solving quadratic equations by factorisation.

What is a Quadratic Equation?

A quadratic equation is an equation that can be written in the form: x² + bx + c = 0, where 'x' is the variable and 'a' is 1 (it's often implied).

Factorisation Method

1. Rearrange the Equation: Make sure the equation is in the standard form: x² + bx + c = 0
2. Find Two Numbers: Find two numbers (let's call them 'p' and 'q') that:
   • Multiply to give 'c' (the constant term)
   • Add up to 'b' (the coefficient of the x term)
3. Factorise: Rewrite the equation as a product of two binomials: (x + p)(x + q) = 0
4. Zero Factor Property: Use the zero factor property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore:
   • x + p = 0 => x = -p
   • x + q = 0 => x = -q

Example

Solve: x² + 5x + 6 = 0

We need two numbers that multiply to 6 and add up to 5. These numbers are 2 and 3.

Therefore: (x + 2)(x + 3) = 0

So, x = -2 or x = -3