 | Algebra - 1839 - 368 pages
...two and two, with their respective signs, is equal to the co-efficient of the third term. The sum pf the products of the roots taken three and three with...co-efficient of the fourth term, taken with a contrary sign, is equal to the sum of the products of the roots taken three and three ; and so on. Finally,... | |
 | Francis Henney Smith - Mathematics - 1841 - 46 pages
...successive formation of the co-efficients of an equation, from the comInflation of the sum of its roots, the sum of the products of the roots, taken two and two, three and three, &c. He appears to have been the first who understood the use of negative roots, and... | |
 | Charles Davies - Algebra - 1842 - 368 pages
...the roots themselves, is equal to the co-efficient of the second term taken with a contrary sign. 2d. The sum of the products of the roots taken two and...signs, is equal to the co-efficient of the third term. The sum of the products of the roots taken three and three with their signs changed, is equal to the... | |
 | John Radford Young - Equations - 1842 - 276 pages
...involving the roots x3, xt, will be Hence the roots themselves will be Now as the coefficient y is the sum of the products of the roots taken three and three, with changed signs, we have but (x3 + xt) = — (r, + Ta). Consequently Hence, by substitution in the foregoing... | |
 | Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...d ..... &c ...... — /; or, the sum of the roots, with the contrary sign, Q,=ab+ac+ad+bc+bd+, &c.; the sum of the products of the roots, taken two and two, R= — abc-\-abd-\-, &c.; the sum of the products of the roots, taken three and three, with the contrary... | |
 | Elias Loomis - Algebra - 1846 - 380 pages
...the sum of all the roots (1 + 2 + 3) with their signs changed. The coefficient of the third term is the sum of the products of the roots taken two and two; thus, 1x2+1X3 + 2X3. The last term k" the product of all the roots (1X2x3) with their signs changed.... | |
 | John Bonnycastle - 1848 - 334 pages
...second term is the sum of the roots with their signs changed. (2.) The coefficient of the third term is the sum of the products of the roots, taken two and two, with their signs changed. (3.) The coefficient of the fourth term is the sum of the products of the roots, taken... | |
 | Stephen Chase - Algebra - 1849 - 348 pages
...the roots with their signs changed (§ 213. 3). (2.) The coefficient of the third term is equal to the sum of the products of the roots taken two and two (§ 213. 4); (3.) that of the fourth term, to the sum of their products taken three and three ; and... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...equation is wanting , the sum of the roots is equal to 0. 3. If the 3rd term of any equation is wanting, the sum of the products of the roots, taken two and two in a product, is equal to 0. 4. If the absolute term is wanting, the product of the roots must be 0,... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...to the sum of all the roots (1+2+3) with their signs changed. The coefficient of the third term is the sum of the products of the roots taken two and two ; thus, 1X2+1X3+2X3=11. The last term is the product of all the roots (1X2X3) with their signs changed.... | |
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... is equal to the sum of the products of the roots taken three and three ; and so on. 
