 | Ormsby MacKnight Mitchel - 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... | |
 | Charles Davies - 1845 - 382 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 two, with their respective signs, is equal to the co-efficient of the third term. 3d. The sum of the products... | |
 | Elias Loomis - 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... | |
 | Stephen Chase - 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 - 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 - 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.... | |
 | Benedict Sestini - 1857 - 258 pages
...with regard to the equations 0, . . . = 0, we will have x — t The coefficient B in [e] is equal to the sum of the products of the roots, taken two and two. If we suppose one of the roots wanting, for instance A, the products of the remaining roots, taken... | |
 | Elias Loomis - 1864 - 386 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. Ex. 2. Form the equation whose roots are 2, 3, 5, and —6. Ans. x ' —4.K'—29x'+156x—... | |
 | James Robert Christie - 1866 - 428 pages
...second term is the sum of all the roots, with their signs changed. The coefficient of the third term is the sum of the products of the roots, taken two and two, with their signs changed. The coefficient of the fourth term is the sum of the products of the roots,... | |
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The sum of the products of the roots taken two and two, with their respective signs, is equal to the co-efficient of the third term. 
