AlgebraTopic Summary
Knowledge Organiser: Solving Quadratic Equations
This topic summary covers Knowledge Organiser: Solving Quadratic Equations within Solving Quadratics for GCSE Mathematics. Revise Solving Quadratics in Algebra for GCSE Mathematics with 15 exam-style questions and 12 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 8 of 8 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 8 of 8
Practice
15 questions
Recall
12 flashcards
Knowledge Organiser: Solving Quadratic Equations
Key Terms
- Quadratic equation: An equation of the form ax² + bx + c = 0
- Root / solution: The value(s) of x that satisfy the equation
- Null factor law: If A × B = 0, then A = 0 or B = 0
- Parabola: The U-shaped graph of a quadratic — roots are where it crosses the x-axis
- Repeated root: When both solutions are the same (parabola touches x-axis)
Must-Know Facts
- ALWAYS rearrange to ax² + bx + c = 0 before factorising
- A quadratic can have 0, 1, or 2 solutions
- From (x + a)(x + b) = 0: solutions are x = −a and x = −b
- If x² = k, then x = +√k or x = −√k
- For x(x + 3) = 0: solutions are x = 0 and x = −3
- Check both solutions by substituting back into the original equation
Key Methods
- Factorising: rearrange to = 0, factorise, set each bracket = 0
- Difference of two squares: x² − k² = 0 → x = ±k
- Simple form: ax² + c = 0 → x² = −c/a → x = ±√(−c/a)
- Use the quadratic formula when factorising is not possible
Common Mistakes
- Not rearranging to = 0 first: You must have ax² + bx + c = 0 before factorising — do not try to factorise with a constant on the right-hand side
- Wrong signs from brackets: From (x + 2)(x − 5) = 0, solutions are x = −2 and x = 5 — the solutions are the opposites of the numbers in the brackets
- Forgetting the negative root: If x² = 9, then x = 3 OR x = −3 — always give both roots unless the context rules one out
- Cancelling x from x² = 3x: Divide only after moving everything to one side — x² − 3x = 0 → x(x − 3) = 0, giving x = 0 and x = 3