Definition:Discriminant of Cubic Equation/Reduced Form/Also presented as

Discriminant of Cubic Equation: Reduced Form: Also presented as

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

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

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.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cubic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cubic