| 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 - 426 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,... | |
| Joseph Ray - 1866 - 420 pages
...coefficient is 0. U. If the 2J term is wanting, the sum of the roots is 0. III. If /lie 3d term is wanting, **the sum of the products of the roots, taken two and two** in a product, is 0. IV. If the absolute term is wanting, the product of the roots must be 0, and hence... | |
| Robert Wallace - 1870 - 164 pages
...coefficient of x"— ' is the sum of the roots taken with a negative sign ; the coefficient of x"—- is **the sum of the products of the roots taken two and two** ; the coefficient of x"—3 is the negative of the sum of the products of the roots taken three and... | |
| Joseph Ficklin - 1874 - 446 pages
...changed is equal lo the sum of the roots (592, 15, 1C) ; 2. The coefficient of the third term is equal to **the sum of the products of the roots, taken two and two** ; 3. T7ie coefficient of the fourth term with its sign changed is equal to the sum of the products... | |
| Michael Angelo McGinnis - 1899 - 207 pages
...again. 331. The coefficients of the second term of the sixth, like all other equations, represents **the sum of the products of the roots, taken two and two.** These combinations will form five cubic equations, as follows : x3 + (ab + cd + ef) x2 + (abed + dbef+... | |
| Samuel Marx Barton - 1899 - 224 pages
...«4"- — «„; that is, the sum of the roots with their signs changed ; the coefficient of x"~- is **the sum of the products of the roots taken two and two** ; the coefficient of x"~3 is the sum of the products of the roots taken three at a time, with their... | |
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