The Discriminant

The Discriminant

From the quadratic formula, we know that the solutions and of a quadratic

equation are given by

$x_{1} = \frac{-b+ \sqrt{b^{2}-4ac}}{2a}$ and $x_{2} = \frac{-b - \sqrt{b^{2}-4ac}}{2a}$ .

The expression b² – 4ac is called the discriminant. When using the quadratic

formula, it is helpful to compute the discriminant first. If it is 0, there

will be just one real solution. If it is positive, there will be two real solutions.

If it is negative, we will be taking the square root of a negative number; hence

there will be two nonreal complex-number solutions, and they will be complex

conjugates.