To determine The maximum possible number of positive and negative roots of 9 x 4 − 12 x 3 − 5 x 2 + 12 x − 4 = 0 . Explanation Definition used: Descartes’ Rule of Signs: 1. 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 ) . 2. 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 9 x 4 − 12 x 3 − 5 x 2 + 12 x − 4 = 0 . Move from left to right, obtain the number of sign changes. From 9 x 4 → − 12 x 3 , − 5 x 2 → + 12 x , and + 12 x → − 4 , there are 3 sign changes. Thus, the number of positive roots is 3. Change the function f ( x ) to f ( − x ) as follows

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 15.3, Problem 1PE

To determine

The maximum possible number of positive and negative roots of 9x4−12x3−5x2+12x−4=0.

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Chapter 15.2, Problem 32E

Chapter 15.3, Problem 2PE

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