GCSE Mathematics Revision — Quadratic Equations
Revise Quadratic Equations for GCSE Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
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What is Quadratic Equations?
A quadratic equation has the form ax² + bx + c = 0. You can solve quadratics by factorising, using the quadratic formula x = (-b ± √(b²-4ac)) / 2a, or completing the square. Factorising is fastest when it works, but the formula always works. The discriminant b²-4ac tells you how many solutions exist: positive means two, zero means one (repeated), negative means none (no real roots).
Board notes: All boards require factorising and the quadratic formula at Higher. Completing the square is also Higher content. AQA sometimes asks students to derive the formula.
Step-by-step explanationWorked examples
Worked example
Solve x² - 5x + 6 = 0. Factorise: (x - 2)(x - 3) = 0. So x = 2 or x = 3.
Practise this topic
Start with low-focus cards for Quadratic Equations, then move into full exam-style practice when you want the heavier session.
Common mistakes
- 1Forgetting to rearrange the equation to = 0 before factorising.
- 2Sign errors in the quadratic formula, especially with the -b term when b is already negative.
- 3Giving only one solution when there are two (forgetting the ± in the formula).
- 4Not checking whether the question asks for exact answers (surds) or decimal approximations.
Quadratic Equations exam questions
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Frequently asked questions
When should I use the quadratic formula instead of factorising?
Use the formula when the quadratic does not factorise neatly, or when the question specifically asks for answers to a given number of decimal places or significant figures.
What does the discriminant tell you?
The discriminant is b² - 4ac. If it is positive, there are two distinct real roots. If zero, there is one repeated root. If negative, there are no real roots.