To determine The maximum possible number of positive and negative roots of 4 x 5 + x 4 + 4 x 3 − x 2 + 5 x + 6 = 0 after changing its signs. Explanation 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 4 x 5 − x 4 − 4 x 3 + x 2 − 5 x − 6 = 0 . After changing the signs, the equation becomes 4 x 5 + x 4 + 4 x 3 − x 2 + 5 x + 6 = 0 . Move from left to right, obtain the number of sign changes. From + 4 x 3 → − x 2 and − x 2 → + 5 x , there are 2 sign changes. Thus, the number of positive roots is 2. 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 1E

To determine

The maximum possible number of positive and negative roots of 4x5+x4+4x3−x2+5x+6=0 after changing its signs.

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Chapter 15.3, Problem 2PE

Chapter 15.3, Problem 2E

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