Quadratic equations: GCSE Maths revision
A quadratic equation can be written ax² + bx + c = 0. Solve by factorising, the quadratic formula, or completing the square. Always check by substituting.
Factorising
Solve x² + 5x + 6 = 0
Quadratic formula
This is not always on the formula sheet — memorise it. If the discriminant b² − 4ac is negative, there are no real solutions.
Try these questions
Cover the answers and have a go first. Worked solutions are underneath.
Solve x² + 7x + 12 = 0 by factorising
Solve x² − 9 = 0
Solve x² − 5x = 0
Use the formula to solve x² + 4x + 1 = 0, leaving answers in surd form
How many real solutions does x² + 2x + 5 = 0 have?
Common mistakes
- Forgetting the negative root.
- Dividing only part of the formula by 2a.
- Not rearranging to = 0 before factorising.
Answers and working
Frequently asked questions
When do I use the formula?
When the quadratic does not factorise nicely, or the question asks for answers to a given number of decimal places.
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