I notice many students forget how discriminant works! I think I should inform A-level students that they need to know how it works and that is one thing they should not return to their O-level teachers. So I thought I share a bit on how to effectively, get it correct and also use it. At the same time, I hope to better the students’ understanding too.

Let us first look at the quadratic formula that is well engrained in our heads.

$x= \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$

Now do we see a very familiar formula in there? Yes, its our discriminant formula, $b^{2}-4ac$!!! So how does it work, alongside with roots. Let’s look at what a root is next, a root is loosely put, a solution to the equation. I hope it is slowly making sense.

When the discriminant is negative, we have a $\sqrt{-\mathrm{number}}$ which is imaginary, that means we have NO real roots!!

And when the discriminant is zero, we have $\sqrt{0}=0$ so we only have one single root, that is $-\frac{b}{2a}$.

BUT if we have a positive discriminant, than due to the $\pm{ }$ there, we end up with two roots.

So I do hope this clears up the air as to how we can relate some algebra with roots. 🙂

This is a question worth looking at from A-levels which test us on discriminant.