Discriminant of a Polynomial
Discriminant of a Polynomial
This Demonstration shows the discriminant of the polynomial . The discriminant of a polynomial of degree is the quantity R(p,p')/, 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.
p(x)=++⋯+x+
a
n
n
x
a
n-1
n-1
x
a
1
a
0
n
n(n-1)/2
(-1)
a
n
p'
p
R(p,q)
p
q
p
p