Solve (x − 3)(x + 4) = 0.

x = 3 or x = −4. Each bracket in turn equals zero.

x = 3 or x = −3. (x + 3)(x − 3) = 0.

Solve x² + 5x + 4 = 0.

x = −1 or x = −4. (x + 1)(x + 4) = 0.

For x² + 2x − 5 = 0, what is the value of b² − 4ac?

24. 2² − 4 × 1 × (−5) = 4 + 20.

What is x² + 6x in completed-square form?

(x + 3)² − 9. Halve the 6, then take off 3².

Quadratic equations · Cambridge IGCSE Mathematics revision

In plain words

A quadratic has an x² in it, and it usually has two answers, because its graph is a curve that can cross the axis twice. If it factorises, the answers drop straight out. If it doesn't, there's a formula that always works.

Three things to know

Factorising: get everything on one side equal to zero, factorise, and set each bracket to zero. (x − 2)(x − 3) = 0 gives x = 2 or x = 3.
The formula: for ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) ÷ 2a.
Completing the square: x² + 6x + 2 = (x + 3)² − 7. This also shows the turning point of the graph, at (−3, −7).

Worked example

Solve x² + 3x − 10 = 0.

Factorise: two numbers that multiply to −10 and add to 3 are 5 and −2, so (x + 5)(x − 2) = 0.
Either x + 5 = 0 or x − 2 = 0.
x = −5 or x = 2.

Tips and tricks

The signs in the answers are the opposite of the signs in the brackets.
"Give your answers to 2 decimal places" is a hint that it won't factorise: use the formula.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Quadratic equations: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

Solve (x − 3)(x + 4) = 0.
- x = −3 or x = 4
- x = 3 or x = −4 (the answer)
- x = 3 or x = 4
- x = 12
Each bracket in turn equals zero.
Solve x² − 9 = 0.
- x = 3 only
- x = 9
- x = 3 or x = −3 (the answer)
- x = 4.5
(x + 3)(x − 3) = 0.
Solve x² + 5x + 4 = 0.
- x = 1 or x = 4
- x = −1 or x = −4 (the answer)
- x = 5 or x = 4
- x = −5
(x + 1)(x + 4) = 0.
For x² + 2x − 5 = 0, what is the value of b² − 4ac?
- −16
- 4
- 24 (the answer)
- 29
2² − 4 × 1 × (−5) = 4 + 20.
What is x² + 6x in completed-square form?
- (x + 6)² − 36
- (x + 3)² − 9 (the answer)
- (x + 3)² + 9
- (x + 6)²
Halve the 6, then take off 3².

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

4 questions, 9 marks. Write your answers on paper, then check them.

Quadratic equations

Cambridge IGCSE Mathematics 0580 · 9 marks · papermunch.org

Name ______________________________ Date ______________

Solve x² − 5x + 6 = 0.[2]
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x = 2 or x = 3.
I got this one
Solve x² = 7x.[2]
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x = 0 or x = 7. x(x − 7) = 0.
I got this one
Solve x² − 4x + 1 = 0, giving your answers to 2 decimal places.[3]
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x = 3.73 or x = 0.27. (4 ± √12) ÷ 2.
I got this one
Write x² + 4x − 1 in the form (x + a)² + b.[2]
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(x + 2)² − 5.
I got this one

Answers: Quadratic equations

1. x = 2 or x = 3.
2. x = 0 or x = 7. x(x − 7) = 0.
3. x = 3.73 or x = 0.27. (4 ± √12) ÷ 2.
4. (x + 2)² − 5.