B. Additional Tests for Zeros of a Polynomial Function
B.1 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 of the function it is possible to determine the maximum number of positive zeros and the maximum number negative zeros by examining the sign changes in consecutive coefficients in f(x). We say that a variation of sign occurs when two consecutive coefficients have opposite signs. For example, in the polynomial
there are three variations of sign: between the first and second coefficients, between the third ...
Get Precalculus with Calculus Previews, 6th Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
