Discriminant of a Polynomial

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows the discriminant of the polynomial . The discriminant of a polynomial of degree is the quantity , where is the derivative of and is the resultant of and . The resultant is equal to the determinant of the corresponding Sylvester matrix. The discriminant of is 0 if and only if has a multiple root.

Contributed by: Izidor Hafner (December 2016)
Open content licensed under CC BY-NC-SA



The discriminant of a polynomial with leading coefficient 1 is the product over all pairs of roots , of .

The equation relates the discriminant and resultant.

To calculate the discriminant, we use the built-in Mathematica function Discriminant. The other way is to calculate the resultant using the Sylvester matrix and then the discriminant from the above equation.

For the meaning of the matrix/grid, see Sylvester Matrix (Wolfram MathWorld).


[1] E. J. Borowski and J. M. Borwein, Dictionary of Mathematics, London: Collins, 1989 p. 169.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.