The Discriminant is part of the quadratic equation:

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

The discriminant $=b^2-4ac$

The cool thing about the discriminant is that it tells us the number of solutions of a quadratic equation that is set equal to zero. There are three possible scenarios:

If $b^2-4ac>0$, the quadratic equation has two solutions.

If $b^2 -4ac=0$, the quadratic equation has one solution.

If $b^2-4ac<0$, the quadratic equation has zero solutions.

The reason why a negative discriminant has zero solutions comes from our earlier arithmetic knowledge. Recall that we cannot have a negative value under a radical.