Discriminant of a Polynomial
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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
Snapshots
Details
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).
Reference
[1] E. J. Borowski and J. M. Borwein, Dictionary of Mathematics, London: Collins, 1989 p. 169.
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