Watch out
Using b without its negative sign.
Scottish National 5 Mathematics
National 5 Maths Quadratic formula
Use the quadratic formula accurately, including careful sign handling and rounding.
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 as ax² + bx + c = 0 and identify signed a, b and c
- Enter the whole numerator in brackets and evaluate the plus and minus cases separately.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Quadratic formula is an assessed part of Scottish National 5 Mathematics in the algebra area. Use the quadratic formula accurately, including careful sign handling and rounding.
Write the equation as ax² + bx + c = 0 and identify signed a, b and c
Substitute into one complete fraction with brackets.
Calculate both the plus and minus roots and round only as instructed.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Visual support
Substitute into the quadratic formula
ax² + bx + c = 0
x =
For x² + 5x + 3 = 0: a = 1, b = 5, c = 3
Key formulae and rules
- x =
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.
Calculator tip
Enter the whole numerator in brackets and evaluate the plus and minus cases separately.
Worked examples
Worked example 1
Quadratic formula worked example
Solve x² + 4x − 1 = 0.
- a = 1, b = 4, c = −1
- x =
Answer: x = −2 ± √5
Watch out
- Using b without its negative sign.
- Dividing only the square-root term by 2a.