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
\(D>0\)
\(D=0\)
\(D<0\)
