AS Maths Core 1 Solving Quadratic Equations

There are many ways to solve quadratics! Here are the ways we’ll look at today… –Factorising (quickest method, but doesn’t always work) –Quadratic Formula (long and tedious, but never fails!) –Completing the Square (useful when sketching b/c it allows you to find vertex) Methods

When we factorise a quadratic expression, we typically end up in the form (x + a)(x + b), where a and b are integers. If we are asked to solve a quadratic in the form (x + a)(x + b) = 0, we can set each factor equal to zero and solve separately. Why? Because we know that if we have two unknown values being multiplied and they = 0, then one or both of the values must equal zero. If (a)(b) = 0, then either a or b or both is zero. Method 1: Factorising

Must be in standard form & set equal to zero! Factorise fully Set each factor equal to zero and solve separately Solving Quadratics Steps...

Solve. (a) (b) (c) Example 1: Already in Factorised Form Divide both sides by -2

Solve. (a) (b) Example 2: Factorise then solve

Solve. (c) (d) Example 2: Factorise then solve (cont’d)

Method 2: Completing the Square EXPRESS THE FOLLOWING IN COMPLETED SQUARE FORM, AND USE YOUR RESULT TO SOLVE THE EQUATION. Next, make x the subject! Remember, the answer can be positive or negative! Since this is a non-calculator exam, leave answer in simplest surd form.

You try… 1.2. Complete the square for the following quadratics:

Exam Question

Solution (a) (b)

Complete the worksheet to practise Method 3: Quadratic Formula