IGCSE Maths Quadratic Equations Notes
A quadratic equation has an x² term. Solve it by factorising, using the quadratic formula, or completing the square.
Key concepts
- Standard form
- Rearrange to ax² + bx + c = 0 before solving.
- Factorising
- Find two brackets that multiply to give the quadratic, then set each to zero.
- Quadratic formula
- Solves any quadratic, especially when it will not factorise neatly.
Key formulas
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a
Discriminant
b² − 4ac
Positive = two roots, zero = one, negative = none.
Worked example
Solve x² − 5x + 6 = 0.
- 1Find two numbers that multiply to 6 and add to −5: −2 and −3.
- 2Factorise: (x − 2)(x − 3) = 0.
- 3Set each bracket to zero: x = 2 or x = 3.
Answer: x = 2 or x = 3
Common mistakes
✗ Not setting the equation to zero first.
✓ Rearrange to ax² + bx + c = 0 before factorising or using the formula.
✗ Giving only one solution.
✓ A quadratic usually has two solutions — state both.
✗ Sign slips in the quadratic formula.
✓ Use brackets around −b and (b² − 4ac) when keying into a calculator.
Quick check
Try these, then reveal the answers.
Solve x² − 9 = 0.Reveal answer
x = 3 or x = −3
Solve x² + 2x − 8 = 0.Reveal answer
x = 2 or x = −4
Discriminant of x² + x + 1?Reveal answer
−3 (no real roots)
Exam tips
- Try factorising first; only use the formula if it will not factorise neatly.
- Round formula answers to the accuracy the question asks for (often 3 s.f.).
- If asked to complete the square, write in the form (x + p)² + q.
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Frequently asked questions
When should I use the quadratic formula?+
Use it when the quadratic will not factorise easily, or when the question demands decimal solutions.
What does the discriminant tell me?+
b² − 4ac shows how many real solutions there are: positive gives two, zero gives one, negative gives none.
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