## What is the discriminant?

The discriminant of a quadratic is closely linked to the Quadratic Formula. For a general quadratic \(ax^2+bx+c\), the discriminant, \(D\), is \[D=b^2-4ac\] You can easily see where this comes from in the Quadratic Formula \[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

\(D>0\)

Two distinct roots

\(D=0\)

One repeated root

\(D<0\)

No real roots

The case \(D<0\) can be seen to have no real roots because in the quadratic formula, it would result in square rooting a negative value which cannot give a real answer.

## Visual examples for various discriminants

\(D>0\)

\(D=0\)

\(D<0\)