An easier approach to remembering discriminant

I notice manyΒ 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. πŸ™‚

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

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