quadratic formula , discriminant

The quadratic formula can find the x-intercepts (roots) of a quadratic. It is ==$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$==.

The discriminant ($\Delta$) of a polynomial determines the number of x-intercepts (roots). It is calculated with $b^2-4ac$.

• $\Delta <0$ means no real solutions, $\Delta =0$ means one solution, $\Delta >0$ means two solutions.
• If $\Delta$ is a perfect square then the solution is rational.