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" From this we might conclude that every equation involving but one unknown quantity, has as many roots as there are units in the exponent of its degree, and can have no more. "
New University Algebra: A Theoretical and Practical Treatise, Containing ... - Σελίδα 359
των Horatio Nelson Robinson - 1864 - 420 σελίδες
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - 1811 - 404 σελίδες
...to equations of higher or lower dimensions : viz, that in general an equation of any degree whatever has as many roots as there are units in the exponent of the highest power of the unknown quantity, and that each root has the property of rendering, by its...

A Course of Mathematics: For the Use of Academies as Well as ..., Τόμος 2

Charles Hutton - 1812 - 624 σελίδες
...to equations of higher or lower dimensions : viz, that in general an equation of any degree whatever has as many roots as there are units in the exponent of the highest power of the unknown quantity, und that each root has the properly of rendering, by its...

A Course of Mathematics for the Use of Academies, as Well as Private Tuition

Charles Hutton - 1822 - 680 σελίδες
...to equations of higher or lower dimensions : viz. that in general an equation of any degree whatever has as many roots as there are units in the exponent of the highest power of the unknown quantity, and that each root has the property of rendering, by its...

Elements of Algebra: Tr. from the French of M. Bourdon, for the Use ..., Τόμος 1

Bourdon (M., Louis Pierre Marie) - 1831 - 446 σελίδες
...the 4th term is (a3 +Pa+Q)a+R, or a3 +Pa3+Qa+H. This law should be remembered. 254. Second property. Every equation involving but one unknown quantity, has as many roots as there are units in ihe exponent of its degree, and no more. Let the proposed equation be Since (No. 250) every equation...

Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ...

Charles Davies - 1835 - 378 σελίδες
...the 4th term is (a3+Pa+Q)a+R, or o'+Pa3+ Qa+R. This law should be remembered. Second Property. 264. Every equation involving but one unknown quantity,...there are units in the exponent of its degree, and no more. Let the proposed equation be if+Par-i+Q«" 3+ • • . +Tx+\J=0. Since every equation has...

On the theory and solution of algebraical equations

John Radford Young - 1835 - 302 σελίδες
...form /(«)»«(«_«)/,(*)! FUNDAMENTAL PttOPERTIES PROPOSITION III. (6.) Every equation containing but one unknown quantity has as many roots as there are units in the number denoting its degree, that is, an equation of the nth degree has n roots. Let an equation of...

Elements of Algebra

1838 - 372 σελίδες
...the 4th term is (a2+Pa+Q)a+R, or a2+Paa+Qa+R. > This law should be remembered. Second Property. 281. Every equation involving but one unknown quantity,...there are units in the exponent of its degree, and no more. Let the proposed equation be xn+Pxm~l+Q.xm-2+ . . . +Ta;+U=0. Since every equation has at...

Elements of Algebra

1839 - 368 σελίδες
...should be remembered. Second Property. 281. Every equation involving but one unknown quantity, has at many roots as there are units in the exponent of its degree, and no more. Let the proposed equation be 'tfa+Pxm-l+Qxm-3+ . . . +Ta;+U=0. Since every equation has at...

Elements of Algebra

Charles Davies - 1842 - 368 σελίδες
...should be remembered. Second Property. 281. Every equation involving but one unknown quantity, has at many roots as there are units in the exponent of its degree, and no more. Let the proposed equation be af+Px " - l +Qx m -3+ . . . +Ta;+U=0. Since every equation has...

Elements of Algebra: Including Sturms' Theorem

Charles Davies - 1845 - 382 σελίδες
...2 and 3 : find the equation containing the other roots. Ans. 4x2 + 6a;+ 1 =0. Second Property. 280. Every equation involving but one unknown quantity,...has as many roots as there are units in the exponent which denotes its degree, and no more. Let the proposed equation be a;™ + Ps"--i + Qs™-2 + . ....




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