Quadratic Equations

When \(a \ne 0\) , there are two solutions to \(ax^2 + bx + c = 0\) and they are
\[x = {-b \pm \sqrt{b^2-4ac} \over 2a}.\]

Discriminant: \(D = b^2-4ac\)

If \(\alpha\) and \(\beta\) are the roots of quadratic equation (\(ax^2 + bx + c = 0\)), then:

• \(\alpha + \beta = -{b \over a}\)
• \(\alpha \beta = {c \over a}\)
• \((x - \alpha)(x - \beta) = 0\)