AlgebraFoundation and Higher

Quadratic equations: GCSE maths practice with worked answers

Show Working has 2 kinds of quadratic equations question for GCSE Maths, for Foundation and Higher. Every question is new each time and comes with the working, step by step.

A quadratic equation has an x² term. At GCSE you solve them by factorising into two brackets, then setting each bracket equal to zero, which usually gives two answers.

Coming soon to the App Store

Worked example 1: solve a quadratic given as brackets

Solve (x − 9)(x − 7) = 0.

Two things multiplied together make 0, so one of them must be 0.
x−9 = 0 gives x = 9.
x−7 = 0 gives x = 7.
The answers are x = 9 and x = 7.

Answer x = 9, x = 7

01 / What's covered2 kinds of question

Quadratic equations questions in the app

Each kind makes fresh questions every time, so you can practise as often as you like.

Solve a quadratic given as bracketsBoth tiers
Solve a quadratic by factorisingBoth tiers

Worked example 2: solve a quadratic by factorising

Solve x² + 3x − 10 = 0.

Factorise: you need two numbers that multiply to −10 and add to 3. They are 5 and −2, so x² + 3x − 10 = 0 becomes (x + 5)(x − 2) = 0.
Set each bracket equal to 0: x + 5 = 0 gives x = −5, and x − 2 = 0 gives x = 2.

Answer x = −5, x = 2

A common mistake

Giving only one answer, or the wrong signs. If (x − 9)(x − 7) = 0 then x = 9 or x = 7, not −9 and −7.

02 / Practise itiPhone and iPad

Practise quadratic equations in Show Working

In the app, open Topics and choose Quadratic equations for ten fresh questions. Ask for a hint if you are stuck, and open the working to see the method one step at a time.