Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a
The quadratic formula is x = (−b ± √(b² − 4ac)) / 2a.
What each letter means
- \(a,\ b,\ c\) the numbers in ax² + bx + c = 0 (a is not 0)
- \(x\) the solutions (roots) of the equation
- \(b^2-4ac\) the discriminant: it tells you how many real roots there are
When to use it
To solve any quadratic equation ax² + bx + c = 0, especially one that does not factorise. Rearrange so that one side is 0 before you read off a, b and c.
Worked example
Solve \(x^2-6x+4=0\), giving your answers to 2 decimal places.
- \(a=1,\ b=-6,\ c=4\)
- \(x=\dfrac{6\pm\sqrt{36-16}}{2}=\dfrac{6\pm\sqrt{20}}{2}\)
Answer: \(x=5.24\) or \(x=0.76\)
Common mistake
Losing a minus sign. If b = −3, then −b = 3 and b² = 9, not −9. Put negative values in brackets when you substitute.
On your course
| Course | In the exam |
|---|---|
| Edexcel 4MA1 (Higher) | On the formulae page of the Higher papers |
| Cambridge 0580 | On the list of formulas in Extended papers (Extended only) |
From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).
Practise and revise
- Practise 4MA1 quadratic equations questions
- Practise 0580 quadratic equations questions
- Revise Algebra notes
- Print Edexcel 4MA1 (Higher) one-page formula sheet
Questions
What is the quadratic formula?
The quadratic formula is x = (−b ± √(b² − 4ac)) / 2a. a, b, c: the numbers in ax² + bx + c = 0 (a is not 0); x: the solutions (roots) of the equation; b²-4ac: the discriminant: it tells you how many real roots there are.
Is the quadratic formula given in the exam?
Edexcel 4MA1 (Higher): on the formulae page of the Higher papers. Cambridge 0580: on the list of formulas in Extended papers (Extended only). This comes from our own IGCSE Maths formula sheets; your teacher has the official booklet.
What does the discriminant tell you?
If b² − 4ac is positive there are two different real roots, if it is 0 there is one repeated root, and if it is negative there are no real roots.
Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.