Edexcel International GCSE Mathematics A · 4MA1
Quadratic equations
A quadratic equation contains a squared variable and can have two real solutions, one repeated solution or no real solutions. Factorising is efficient when the expression splits into simple brackets. First collect every term on one side so the other side is zero.
Key method
For x² + bx + c, find two numbers with sum b and product c. The zero-product rule applies only when the product equals zero.
Worked example
Solve x² + x − 12 = 0.
- 3 × (−4) = −12, but 3 − 4 = −1; those signs do not give the required middle term.
- Use 4 and −3 instead: (x + 4)(x − 3) = 0.
- Set each bracket equal to zero and check both values in the original equation.
Answer and interpretation
x = −4 or x = 3.
Common mistake
Writing the factors as the answers reverses both solution signs.
Practise independently
Solve x² − 2x − 15 = 0 without a calculator.
Check your answer
(x − 5)(x + 3) = 0, so x = 5 or −3.
Syllabus connection
This lesson develops quadratic equations by factorising within the algebra area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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