Descartes's Rule of Signs
Descartes's Rule of Signs
Descartes's rule of signs estimates the greatest number of positive and negative real roots of a polynomial .
p(x)=++⋯+x+
a
n
n
x
a
n-1
n-1
x
a
1
a
0
Delete any zeros in the list of coefficients and count the sign changes in the new list. If the number of changes is , then the maximum number of positive roots is one of , , ….
m
m
m-2
To get the maximum number of negative roots, use the same procedure for . The coefficients for and are shown in the second and third rows of the table.
p(-x)
p(x)
p(-x)