Definition:Discriminant of Cubic Equation/Reduced Form

Theorem

Let $P$ be a cubic equation expressed in the form:

$x^3 + p x^2 + q x + r = 0$

The discriminant of $P$ is given by:

$D = 4 q^3 + 4 p^3 r + 27 r^3 - p^2 q^2 - 18 p q r$

Also presented as

Some sources present the discriminant of $P$ in the form:

$D = p^2 q^2 + 18 p q r - 4 q^3 - 4 p^3 r - 27 r^3$

under which regime the sign of $D$ is interpreted inversely.