Algebra II Essentials For Dummies by Mary Jane Sterling

Author:Mary Jane Sterling
Language: eng
Format: epub, pdf
ISBN: 9781119590927
Publisher: Wiley
Published: 2019-05-14T00:00:00+00:00

Counting the possible number of negative roots

Along with the positive roots (see the previous section), Descartes’ rule of signs deals with the possible number of negative roots of a polynomial. After you count the possible number of positive roots, you combine that value with the number of possible negative roots to make your guesses and solve the equation.

Descartes’ rule of signs (part II): The polynomial has at most n roots. Find , and then count the number of times the sign changes in and call that value q. The value of q is the maximum number of negative roots of f. If the number of negative roots isn’t q, the number is , , and so on, for as many multiples of 2 as necessary. Again, you count a multiple root as many times as it occurs when applying the rule.

Determine the possible number of negative roots of the polynomial .

You first find by replacing each x with and simplifying:

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