 | 1801 - 520 sider
...equation. % 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 Trail - 1812 - 216 sider
...viz. x— — .f It. is one of the abfur" dities introduced into algebra in the laft age, to fuppofe every equation has " as many roots as there are units in the index of its highefl power, and * 'confequently that every quadratic equation has two : but the contrary,... | |
 | John Radford Young - 1838 - 368 sider
...(prop. 1 ) ; therefore, the first side of the proposed equation is divisible by x — a. PROPOSITION m. 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 n roots. Let there be x" +... | |
 | John Radford Young - 1839 - 332 sider
...(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"... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 sider
...hence the two values of x are x = 2, x — — у в (285.) It is shown in the theory of equations that every equation has as many roots as there are units in its degree ; and hence x has three values in the equation ж3 = z, and will have three values for every... | |
 | John Radford Young - 1842 - 276 sider
...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 sider
...— 2) 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 sider
...Q,, we have V = (x — a) Q. = 0, which may be satisfied by making x — a = 0, that is x = a. 136. Every equation has as many roots as there are units in the index of the highest power of the unknown quantity. Let a be a root of the equation 3? + Ax" .... Px... | |
 | Samuel Alsop - 1848 - 336 sider
...Q, we have :у=(ж — a)a = o, which may be satisfied by making ж — a = 0, that is x = a. 136. Every equation has as many roots as there are units in the index of the highest power of the unknown quantity. Let a be a root of the equation x" + Aar— •'... | |
 | Stephen Chase - 1849 - 348 sider
...seen (§ 213. 2) that every equation of the second degree has two roots. It will be proved hereafter, that every equation has as many roots as there are units in its degree. See 1, above. The above process, however, does not always exhibit all the roots. § 222.... | |
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He spoke of imaginary quantities, and inferred by induction that every equation has as many roots as there are units in the number expressing its degree. 
