Year 10: Solve the quadratic equation 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: $x^2+bx+c=0$
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:
   • $x+p=0\Rightarrow x=-p$
   • $x+q=0\Rightarrow x=-q$

Example

Solve: $x^2+5x+6=0$

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 $x=-3$