Edexcel International GCSE Mathematics A · 4MA1
The quadratic formula
The quadratic formula solves equations that are awkward to factorise. Write ax² + bx + c = 0 before identifying the coefficients. It also reveals whether real roots exist through the discriminant b² − 4ac.
Key method
Use x = (−b ± √(b² − 4ac))/(2a). A negative discriminant means there are no real roots; zero means a repeated root.
Worked example
Solve 2x² + 3x − 1 = 0 exactly.
- Identify a = 2, b = 3 and c = −1.
- The discriminant is 3² − 4(2)(−1) = 17.
- Substitute into the formula, keeping the whole numerator above 2a = 4.
Answer and interpretation
x = (−3 + √17)/4 or x = (−3 − √17)/4.
Common mistake
Using c = 1 instead of −1 changes the discriminant and the roots.
Practise independently
How many real roots does x² + 2x + 5 = 0 have?
Check your answer
None: the discriminant is 4 − 20 = −16.
Syllabus connection
This lesson develops the quadratic formula 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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