Quadratic Equations — GCSE Mathematics Revision
Revise Quadratic Equations for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
At a glance
- What StudyVector is
- An exam-practice platform with board-aligned questions, explanations, and adaptive next steps.
- This topic
- Quadratic Equations in GCSE Mathematics: explanation, examples, and practice links on this page.
- Who it’s for
- Students revising GCSE Mathematics for UK exams.
- Exam boards
- Practice is aligned to major specifications (AQA, Edexcel, OCR, WJEC, Eduqas, Cambridge International (CIE), SQA, IB, AP).
- Free plan
- Sign up free to use tutor paths and full feedback on your answers. Pricing
- What makes it different
- Syllabus-shaped practice and progress tracking—not generic AI answers.
Topic has curated content entry with explanation, mistakes, and worked example. [auto-gate:promote; score=75.25]
Next in this topic area
Next step: Completing the Square
Continue in the same course — structured practice and explanations on StudyVector.
Go to Completing the SquareWhat 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 example
Solve x² - 5x + 6 = 0. Factorise: (x - 2)(x - 3) = 0. So x = 2 or x = 3.
Practise this topic
Jump into adaptive, exam-style questions for Quadratic Equations. Free to start; sign in to save progress.
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
Exam-style questions for Quadratic Equations with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
Quadratic Equations exam questionsGet help with Quadratic Equations
Get a personalised explanation for Quadratic Equations from the StudyVector tutor. Ask follow-up questions and work through problems with step-by-step support.
Open tutorFree full access to Quadratic Equations
Sign up in 30 seconds to unlock step-by-step explanations, exam-style practice, instant feedback and on-demand coaching — completely free, no card required.
Try a practice question
Unlock Quadratic Equations practice questions
Get instant feedback, step-by-step help and exam-style practice — free, no card needed.
Start Free — No Card NeededAlready have an account? Log in
Step-by-step method
Step-by-step explanation
4 steps · Worked method for Quadratic Equations
Core concept
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 whe…
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.