# 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)