Precalculus with Calculus Previews, 5th Edition

Appendix B Descartes’ Rule of Signs

Introduction Suppose that y = f(x) is a polynomial function with real coefficients and is arranged in the usual manner of descending powers of x. From this form it is possible to determine the maximum number of positive zeros and the maximum number of negative zeros by examining the variations of sign in f(x). We say that a variation of sign occurs when two consecutive terms have opposite signs. For example, in the polynomial

there are three variations of sign: between the first and second terms, between the third and fourth terms, and between the fourth and fifth terms.

We state the following rule without proof. ...