Descartes' rule of signs

Topic Notes
Descartes' Rule of Signs For a polynomial P(x)P(x):
\bullet the number of positive roots = the number of sign changes in P(x)P(x), or less than the sign changes by a multiple of 2.
\bullet the number of negative roots = the number of sign changes in P(x)P(-x), or less than the sign changes by a multiple of 2.

Note: Before applying the Descartes' Rule of Signs, make sure to arrange the terms of the polynomial in descending order of exponents.

trick of Descates' rule of signs