Vocabulary - Discriminant

The discriminant is $b^2 - 4ac$, the part under the square root in the quadratic formula. It tells you how many real solutions exist.

If $b^2 - 4ac > 0$, you have two distinct solutions. If $b^2 - 4ac = 0$, you have one solution (repeated root). If $b^2 - 4ac < 0$, you have no real solutions (only complex).

Before computing the square root, check the discriminant. If it's negative and you only need real answers, you can skip the calculation.