GCSE & IGCSE maths practice

Quadratic equations questions and answers

A quadratic equation has an $x^2$ term. Get everything on one side so it equals 0, factorise, then set each bracket equal to 0: if $(x - 2)(x - 3) = 0$ then $x = 2$ or $x = 3$ . Most quadratics have two solutions. Type both, separated by a comma.

8 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

Start the questions Quadratic equations: lesson and examples Quadratic equation solver

Where quadratic equations comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: solve quadratic equations algebraically by factorising. Higher only: those that need rearranging first, and ax² + bx + c with a ≠ 1.
Cambridge IGCSE (0580)	Extended only: solve quadratic equations by factorisation, completing the square and the quadratic formula. Core solves them from a graph only.

The method

Rearrange so the equation is (quadratic) = 0.
Factorise.
Set each bracket equal to 0 and solve.
In a context, reject a solution that can't be right (e.g. a negative length).

Quadratic equations questions

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Warm-up

Question 1Warm-upFoundation

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

Question 2Warm-upFoundation

Solve $x^2 + 7x + 12 = 0$

Exam-style

Question 3Exam-styleFoundation

Solve $x^2 - 9 = 0$

Question 4Exam-styleFoundation

Solve $x^2 - 4x = 0$

Question 5Exam-styleFoundation

Solve $x^2 + 2x - 15 = 0$

Question 6Exam-styleHigher

Solve $2x^2 + 7x + 3 = 0$

Challenge

Question 7ChallengeHigher

Solve $x^2 = 3x + 10$

Question 8ChallengeHigher

A rectangle is $x$ cm wide and $(x + 3)$ cm long. Its area is 40 cm². Find $x$ .

x =

Common mistakes

Factorising before making one side 0.
Getting the signs of the solutions wrong: (x + 3) = 0 gives x = −3.
Dividing by x and losing the solution x = 0.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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