 | 1801 - 520 pàgines
...% WILLIAM. FREND, Efq. \ LGEBRAISTS, who deal in negative or impoffible numbcrj, Ji\. fuppofe, that every equation has as many roots as there are units in the highcft index of the unknown number in. the equation. Confequemly, as the roots of an equation are... | |
 | William Nicholson - 1812 - 860 pàgines
...that gcnerality,as it admits only of one root ; while the other quantity, made up of unequal factors, has as many roots as there are units in the index of the power, the root of which is to be extracted. Let us now gee how far what has been said above will... | |
 | John Bonnycastle - 1813 - 444 pàgines
...six roots, and no more ; and so on ; it follows, that an equation of any power whatever niust have as many roots as there are units in the index of its highest term (/). 3. Also, since it appears from prop. 1, that every equation, when all its terms are... | |
 | James Ryan, Robert Adrain - 1824 - 542 pàgines
...root, or value of the unknown quantity, it can then be shown, that any proposed equation will have as many roots as there are units in the index of its highest term, and no more. For let a, according to the assumption here mentioned, be a root of the... | |
 | James Ryan - 1824 - 550 pàgines
...root, or value of the unknown quantity, it can then be shown, that any proposed equation will have as many roots as there are units in the index of its highest term, and no more. For let a, according to the assumption here mentioned, be a root of the... | |
 | John Radford Young - 1839 - 332 pàgines
...(prop. 1) ; therefore, the first side of the proposed equation is divisible by x — a. PROPOSITION HI. Every equation has as many roots as there are units in the num ber denoting its degree ; that is, an equation of the nth degree has л roots. Let there be x"... | |
 | John Radford Young - 1842 - 276 pàgines
...1 5x4 + 69r> — 34 U" + 1 705x — 8526 and the remainder — 2994 PROPOSITION III. THEOREM. (10.) Every equation has as many roots as there are units in the exponent denoting its degree ; that is an equation of the rath degree '+ Ax+N=0 has n roots. In order... | |
 | Ormsby MacKnight Mitchel - 1845 - 308 pàgines
...1.2.3 ' and so on of the divisors of all degrees. 234. As an exemplification of the principle, that every equation has as many roots as there are units in the exponent of the highest power of the unknown quantity, we propose to examine the equation xm—! =0.... | |
 | Samuel Alsop - 1846 - 300 pàgines
...equation. We have already seen that quadratic equations have two roots; we shall hereafter show that every equation has as many roots as there are units in the number of its degree. 135. If a be a root of the equation, then will the left member of this equation... | |
 | Samuel Alsop - 1848 - 336 pàgines
...equation. We have already seen that quadratic equations have two roots; we shall hereafter show that every equation has as many roots as there are units in the number of its degree. 135. If a be a root of the equation, x" + Аж"-1 + Ваг"-2 + .... Pa; -f R... | |
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We have already seen that quadratic equations have two roots; we shall hereafter show that every equation has as many roots as there are units in the number of its degree. 
