Quadratic Functions and Equations in One Variable
Root of an equation
A value of x that makes the equation equal to zero; where the graph meets the x-axis.
| English | Root of an equation |
|---|---|
| Bahasa Melayu | Punca persamaan |
| 中文 | 方程的根 |
How it is used
For x² − 5x + 6 = 0, factorising gives (x − 2)(x − 3) = 0, so the roots are x = 2 and x = 3, the two points (2, 0) and (3, 0) where the parabola cuts the x-axis.
Where it shows up in SPM
Central to solving quadratic equations (Form 4). In Paper 1 you find roots quickly by factorisation; in Paper 2 you may use the formula x = (−b ± √(b² − 4ac))/2a, or read roots off a sketched graph as its x-intercepts.
Don't confuse it with
Open the chapter: Quadratic Functions and Equations in One Variable →
Frequently asked questions
Can a quadratic equation have only one root?
Yes. When b² − 4ac = 0 the two roots are equal, so there is one repeated root and the parabola just touches the x-axis.
For example x² − 6x + 9 = 0 gives (x − 3)² = 0, a single root x = 3.
What if I cannot factorise the equation?
Use the quadratic formula x = (−b ± √(b² − 4ac))/2a, which works for every quadratic. It gives exact roots even when the numbers are not whole; just substitute a, b and c carefully and simplify the surd if needed.
Are roots the same as solutions?
For a quadratic equation, yes, the roots are the solutions, the x-values that make ax² + bx + c = 0 true. On the graph these same values are the x-intercepts where y = 0.