Discriminant of Polynomial/Examples

Examples of Discriminants of Polynomials

Quadratic

Let $\alpha_1$ and $\alpha_2$ be the roots of a quadratic equation $f$.

The discriminant of $f$ is:

$\paren {\alpha_1 - \alpha_2}^2$

Cubic

Let $\alpha_1$, $\alpha_2$ and $\alpha_3$ be the roots of a cubic equation $f$.

The discriminant of $f$ is:

$\paren {\alpha_1 - \alpha_2}^2 \paren {\alpha_2 - \alpha_3}^2 \paren {\alpha_3 - \alpha_1}^2$