A-Level MathsDiscriminants


The discriminant of a quadratic equation will tell you how many roots the quadratic equation has.

Solutions of a quadratic equation are known as roots; they can be seen on the graph of a quadratic where the graph crosses the x-axis. Recall that the general quadratic equation: ax^2+bx+c=0, can have two distinct roots, one repeated roots or no roots at all (unless you are working with complex numbers).

The discriminant can tell you how many roots a quadratic equation will have without having to actually find them.

For the quadratic equation ax^2+bx+c=0, the discriminant is given by b^2-4ac.

If b^2-4ac=0, the equation has one repeated root.
If b^2-4ac=0, the equation has one repeated root.
If b^2-4ac<0, the equation has no roots.