Explanation Result used: “ Descartes’s rule of signs: Let P ( x ) , written in descending order or ascending order, be a polynomial function with real coefficients and a nonzero constant term. The number of positive real zeros of P ( x ) is either: 1 The same number as the number of variations of sign in P ( x ) by a positive even integer. 2 Less than the number of variations of sign in P ( x ) by a positive even integer. The number of negative real zeros of P ( x ) is either: 3 The same number as the number of variations of sign in P ( − x ) by a positive even integer. 4 Less than the number of variations of sign in P ( − x ) by a positive even integer. Calculation: Consider the given polynomial, f ( x ) = x 5 − 2 x 3 − 8 x . The number of variations of sign in f ( x ) is 1

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Chapter 4.4, Problem 94E

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The information Descartes’s rule tell about the number of positive real zeros and the negative number of real zeros.

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Chapter 4.4, Problem 93E

Chapter 4.4, Problem 95E

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