 | Charles Hutton - Mathematics - 1811 - 404 pages
...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... | |
 | Charles Hutton - Mathematics - 1812 - 624 pages
...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... | |
 | Charles Hutton - Mathematics - 1822 - 680 pages
...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... | |
 | Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 446 pages
...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... | |
 | Charles Davies - Algebra - 1835 - 378 pages
...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... | |
 | John Radford Young - 1835 - 302 pages
...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... | |
 | Algebra - 1838 - 372 pages
...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... | |
 | Algebra - 1839 - 368 pages
...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... | |
 | Charles Davies - Algebra - 1842 - 368 pages
...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... | |
 | Charles Davies - Algebra - 1845 - 382 pages
...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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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. 
