[hal-00854254] Some remarks about Descartes’ rule of signs

What can we deduce about the roots of a real polynomial in one variable by simply considering the signs of its coefficients? On one hand we give a complete answer concerning the positive roots by proposing a statement of Descartes' rule of signs which strengthens the available ones while remaining as elementary and concise as the original On the other hand we provide new kinds of restrictions on the combined numbers of positive and negative roots



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