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Precalculus with Calculus Previews, 6th Edition by Dennis G. Zill, Jacqueline M. Dewar

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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:

image

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 ...

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