Explanation Definition used: Descartes’ Rule of Signs: 1. The number of positive zeros of a polynomial equation f ( x ) = 0 cannot be greater than the number of changes in sign in f ( x ) in moving from one term to the next in f ( x ) . 2. The number of negative zeros cannot be greater than the number of sign changes in f ( − x ) . Calculation: It is given that the equation is 2 x 5 − 3 x 4 + 8 x 3 − 4 x 2 − 4 x + 2 = 0 . Here, f ( x ) = 2 x 5 − 3 x 4 + 8 x 3 − 4 x 2 − 4 x + 2 . Move from left to right, obtain the number of sign changes. As there are 4 sign changes, the number of positive roots is 4. Change the function f ( x ) to f ( − x ) as follows

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 15.3, Problem 23E

Chapter 15.3, Problem 25E

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Chapter 15 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

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