Explanation Theorem used: Rational Root Theorem: Any rational root r r of a polynomial equation f ( x ) = a n x n + a n − 1 x n − 1 + ⋯ + a 0 = 0 is an integer factor of a 0 divided by an integer factor of a n . Therefore, r r = integer factor of a 0 integer factor of a n . Definition used: Descartes’ Rule of Signs: The number of positive 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 ) . The number of negative cannot be greater than the number of sign changes in f ( − x ) . Calculation: It is given that the polynomial equation is 2 x 4 + x 2 − 22 x + 8 = 0 . Here, f ( x ) = 2 x 4 + x 2 − 22 x + 8 . Move from left to right, obtain the number of sign changes. As there are 2 sign changes, the number of positive roots is 2. 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 29E

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The possible smallest and largest rational roots of the equation.

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Chapter 15.3, Problem 28E

Chapter 15.3, Problem 30E

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3. Describe the steps you would take to find the absolute max of the following function using Calculus f(x) = : , [-1,2]. Then use a graphing calculator to x-1 x²-x+1 approximate the absolute max in the closed interval.

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Chapter 15 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

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