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" Rule. 324. An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs. "
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... - Page 232
by Benjamin Peirce - 1843 - 284 pages
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Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ...

Charles Davies - Algebra - 1835 - 378 pages
...reciprocal of this proposition is evident. Descartes' Rule. 302. An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs ofitt terms, nor a greater number of negative roots than there are permanences of these signs....
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 300 pages
...even; and if this last term is negative, the number of these roots must be uneven. 197. Theorem. An equation cannot have a greater number of positive roots than there are VARIATIONS in the signs of its terms, nor a greater number of negative roots than there are PERMANENCES of these Demonstration....
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Elements of Algebra

Algebra - 1838 - 372 pages
...reciprocal of this proposition is evident. t Descartes't Rule. 324. An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs....
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Elements of Algebra

Bourdon (M., Louis Pierre Marie) - Algebra - 1839 - 368 pages
...of this proposition is evident. Descartes' Rule. 324. An equation of any degree whatever cannot hone a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs....
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Elements of Algebra

Charles Davies - Algebra - 1842 - 368 pages
...reciprocal of this proposition is evident. Descartes' ' Rule. 324. An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs....
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The Analysis and Solution of Cubic and Biquadratic Equations: Forming a ...

John Radford Young - Equations - 1842 - 276 pages
...surpass. The rule is enunciated as in the following proposition. PROPOSITION XI. THEOREM. (28.) An equation cannot have a greater number of positive roots than there are change* of sign from + to — , and from — to -)- in the series of terms forming its first member....
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Elements of Algebra: Including Sturms' Theorem

Charles Davies - Algebra - 1845 - 382 pages
...reciprocal of this proposition is evident. Descartes' Rule. 327. An equation of any degree whatever, cannot have a greater number of positive roots than there are variations in the signs of its terms, nor a greater number of negative roots than there are permanences of these signs....
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An Elementary Treatise on Algebra: In which the Principles of the Science ...

Samuel Alsop - Algebra - 1846 - 300 pages
...But, by this change of sign, the signs of all the roots are changed. (Art. 1:19.) Hence, since this equation cannot have a greater number of positive roots than there are variations of signs ; it follows that the original equation cannot have a greater number of negative roots than...
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A Treatise on Algebra: In which the Principles of the Science are Familiarly ...

Samuel Alsop - Algebra - 1848 - 336 pages
...degree, the last term of which is negative, has at least two real roots, with contrary signs. 142. An equation cannot have a greater number of positive roots than .there are variations of signs, in successive terms, nor can it have a greater number of negative roots than there are continuations...
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An Elementary Treatise on Algebra

Benjamin Peirce - Algebra - 1851 - 294 pages
...multiplied by every different power of x from the highest to unity, and also a constant term, such as I. 296. Descartes' Theorem. A complete equation cannot...row of signs of its terms, nor a greater number of pf&i'iiv* roots than there are permanences in this row of signs. Proof. If the equation is that of...
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