Quadratic Functions and Equations in One Variable
Discriminant
The value b² − 4ac, whose sign tells you how many real roots a quadratic equation has.
| English | Discriminant |
|---|---|
| Bahasa Melayu | Pembeza |
| 中文 | 判别式 |
How it is used
For x² + 4x + 5 = 0, the discriminant is b² − 4ac = 4² − 4(1)(5) = 16 − 20 = −4. Since it is negative, the equation has no real roots and the parabola never touches the x-axis.
Where it shows up in SPM
Used whenever a question asks about the nature of roots (Form 4). In Paper 1 you compute b² − 4ac and state how many real roots exist; in Paper 2 you often set b² − 4ac = 0, > 0 or < 0 to find an unknown value of a coefficient k.
Don't confuse it with
Open the chapter: Quadratic Functions and Equations in One Variable →
Frequently asked questions
What do the three cases of the discriminant mean?
If b² − 4ac > 0 there are two different real roots; if b² − 4ac = 0 there is one repeated real root; if b² − 4ac < 0 there are no real roots. On the graph these mean the parabola cuts, touches, or misses the x-axis.
Do I have to solve the equation to find the nature of roots?
No. The discriminant lets you decide the number and type of roots without solving.
You only need a, b and c to compute b² − 4ac and check its sign, which saves time in Paper 1.
Why does a negative discriminant mean no real roots?
In the formula the roots contain √(b² − 4ac). If b² − 4ac is negative you would be taking the square root of a negative number, which has no real value, so there are no real roots and the curve stays entirely above or below the x-axis.