2.4 Discriminant of a Quadratic Equation

2.4 Discriminant of a Quadratic Equation

The quadratic equation $ax^2 + bx + c = 0$, where $a \neq 0$ and $a, b, c \in R$ has two roots. Let these roots be $\alpha$ and $\beta$.

Now, $\alpha = \dfrac{-b + \sqrt{b^2 - 4ac}}{2a}$ and $\beta = \dfrac{-b - \sqrt{b^2 - 4ac}}{2a}$

Discriminant

The expression $b^2 - 4ac$, under the radical sign in quadratic formula is called the Discriminant (Disc.) of the equation, $ax^2 + bx + c = 0$. It determines the nature of character of the roots of the equation.