Watch out
Factorising without finding the roots.
Scottish National 5 Mathematics
National 5 Maths Solving quadratic equations
Solve quadratic equations by factorising or by reading roots from a graph.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Write the equation with zero on one side.
- Decide whether a calculator supports the method; exact working may still be required.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Solving quadratic equations is an assessed part of Scottish National 5 Mathematics in the algebra area. Solve quadratic equations by factorising or by reading roots from a graph.
Write the equation with zero on one side.
Factorise completely, then set each factor equal to zero.
For a graph, read the x-coordinates where y = 0.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Key formulae and rules
- If ab = 0, then a = 0 or b = 0.
Check
Check roots by substitution and compare the turning point or discriminant conclusion with the equation's graph.
Exam tip
Keep equations aligned line by line so method marks remain visible, especially through sign and bracket changes.
Worked examples
Worked example 1
Solving quadratic equations worked example
Solve x² − 7x + 12 = 0.
- (x − 3)(x − 4) = 0
- Set each factor equal to zero.
Answer: x = 3 or x = 4
Watch out
- Factorising without finding the roots.
- Forgetting to make the equation equal zero first.