Determining Roots of Polynomials Using Descartes’ Rule of Signs

A detailed tutorial on determining roots of polynomials using Descartes’ rule of signs. Step by step tutorial including several examples of how to determine roots of polynomials using Descartes’ rule of signs for reference.

Descartes’ rule of signs is used to determine the number of positive or negative roots in a polynomial. It does not give the exact number of roots, but it does give a close estimate. There are two versions of this rule – one for positive roots, and one for negative roots. The rule for positive roots states that the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or less than it by a multiple of two. The rule for negative roots states that the number of negative roots is the number of sign changes after negating the coefficients of odd power terms, or less than it by a multiple of two.