Discriminant

The discriminant is a value calculated from a quadratic equation’s coefficients that helps determine the nature of its solutions without actually solving the equation. Specifically, it tells us whether the equation has two real solutions, one real solution (a repeated solution), or no real solutions at all. If the discriminant is positive, there are two distinct real solutions. If it’s zero, there’s exactly one real solution. If it’s negative, the solutions are not real numbers but complex. It’s a useful tool for understanding the solutions’ characteristics quickly.