 Vimit of the positive roots, we have that is, a superior limit of the positive roots is unity, increased by that root of the greatest negative coefficient, whose index is equal to the excess of the degree of the equation above the exponent of the first...  Elementary Treatise on Algebra - Page 235by Benjamin Peirce - 1875Full view - About this book
 | Charles Davies - Algebra - 1835 - 378 pages
...the equation, and will consequently give a positive result for the first member. Therefore vS+1, or unity increased by that root of, the greatest . negative co-efficient whose index is the number of terms which precede the first negative term, is a superior limit of the positive roots... | |
 | Benjamin Peirce - Algebra - 1837 - 300 pages
...must have (x — !)»-«' < (x — 1) x»-»-i < S; and, therefore, or 4 Limits of Negative Roots. . that is, a superior limit of the positive roots is...negative coefficient, whose index is equal to the number of terms which would precede the first negative term, if no terms were wanting. 209. Problem.... | |
 | Benjamin Peirce - Algebra - 1837 - 300 pages
...we, then, denote by L this superior limit of the positive roots, we have Limits of Negative Roots. that is, a superior limit of the positive roots is...by that root of the greatest negative coefficient, lohose index is equal to the number of terms irhich would precede the first negative term, if no terms... | |
 | Algebra - 1838 - 372 pages
...equation, and will consequently give a positive result for the first member. n Therefore \/S+1, or unity increased "by that root of the greatest negative co-efficient whose index is the number of terms which precede the first negative term, is a superior limit of the positive roots... | |
 | Charles Davies - Algebra - 1842 - 368 pages
...the equation, and will consequently give a positive result for the first member. s Therefore VS+l, or unity increased by that root of the greatest negative co-efficient whose index is the number of terms which precede the first negative term, is a superior limit of the positive roots... | |
 | Charles Davies - Algebra - 1845 - 382 pages
...terms of the equation, and will consequently give a positive result for the first member. Therefore, Unity increased by that root of the greatest negative co-efficient whose index is the number of terms which precede the first negative term, is a superior limit of the positive roots... | |
 | Benjamin Peirce - Algebra - 1851 - 294 pages
...i<S; and, therefore, n —m Limits of Negative Roots. If we, then, denote by L this superior limit of the positive roots, we have that is, a superior...unity, increased by that root of the greatest negative coefficienti whose index is equal to the excess of the degree of the equation above the exponent of... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...terms in the parenthesis would be less than x x—l ' ART. 417. PROP. II. — If we increase by unity that root of the greatest negative coefficient, whose index is equal to the number of terms preceding the first negative term, the result will lie greater than the greatest positive... | |
 | Benjamin Peirce - Algebra - 1855 - 308 pages
...Negative Roots. If we, then, denote by L this superior limit of the positive roots, we have L = I +V 8; that is, a superior limit of the positive roots is...roots. Solution. Substitute in the given equation for x, the value and find, by the preceding article, a superior limit of the positive values of y, after... | |
 | Benjamin Peirce - Algebra - 1864 - 298 pages
...Negative Roots. If we, then, denote by // this superior Mniit of the positive roots, we have L=1+~JS; that is, a superior limit of the positive roots is...roots. Solution. Substitute in the given equation for x, the value 1 * = -y' and find, by the preceding article, a superior limit of the positive values... | |
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