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Descartes's Rule of Signs

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Descartes's rule of signs estimates the greatest number of positive and negative real roots of a polynomial .

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Delete any zeros in the list of coefficients and count the sign changes in the new list. If the number of changes is , then the maximum number of positive roots is one of , , ….

To get the maximum number of negative roots, use the same procedure for . The coefficients for and are shown in the second and third rows of the table.

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Contributed by: Izidor Hafner (January 2017)
Open content licensed under CC BY-NC-SA

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