## Precalculus (6th Edition) Blitzer

In the quadratic formula, $x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ we have a radicand, $b^{2}-4ac$, which may be positive, zero, or negative. The number of real solutions depends on its value, because a square root is taken from it. The expression is called the discriminant, and when it is - positive, there will be two distinct real solutions to the quadratic equation, - zero, there will be one real solution (double real zero) - negative, there will be no real solutions (the solutions are complex conjugates)