 | John Bonnycastle - 1818 - 326 pages
...equations above-mentioned, we may here farther add, 1. That the sum of all the roots of any equation is equal to the coefficient of the second term of that equation, with its sign changed. OF THE RESOLUTION or SIMPLE EQUATIONS, Containing only one unknown Quantity. The resolution of simple,... | |
 | James Ryan, Robert Adrain - 1824 - 542 pages
...consequently, the following relations between the coefficients and roots will be sufficiently obvious. I. The sum of all the roots of any equation, having its...coefficient of the second term of that equation, with its tign changed* II. The sum of tht products of all the roots, taken two and two, is equal to the coefficient... | |
 | John Bonnycastle - 1825 - 336 pages
...equations abovementioned, we may here farther add: 1. That the sum of all the roots of any equation is equal to the coefficient of the second term of...with its sign changed. 2. The sum of the products of every two of the roots, is equal to the coefficient of the third terms, without any change in its sign.... | |
 | James Ryan - 1826 - 430 pages
...obvious. I. The sum of a// the roots of any equation, having its terms arranged according to the order oj the powers of the unknown quantity, is equal to the...coefficient of the second term of that equation, with, its lign changed. II The sum of the /iroducts of all the rooti, taken two and two, is equal to the coefficient... | |
 | John Bonnycastle - 1834 - 330 pages
...equations above-mentioned, we may here farther add : 1. That the sum of all the roots of any equation is equal to the coefficient of the second term of...with its sign changed. 2. The sum of the products of cve.rv two of the roots, is equal to the coefririunt of the third term, without any change in its sign.... | |
 | James Ryan, Robert Adrain - 1835 - 388 pages
...relations between the coefficients and roots will be sufficiently obvious. I. The sum of all the Tools of any equation, having its terms arranged according...second term of that equation, with its sign changed. II. The sum of the products of all the roots, taken two and two, is equal to the coefficient of the... | |
 | John Bonnycastle - 1836 - 296 pages
...above mentioned, we may here further add, 1. That the sum of all the roots of any equation is equal Io the coefficient of the second term of that equation,...with its sign changed. 2. The sum of the products of every two of the roots is equal to the coefficient of the third term, without anv change in the sign.... | |
 | John Bonnycastle - 1837 - 296 pages
...equations abovementioned, we may here farther add : — 1. That the sum of all the roots of any equation is equal to the coefficient of the second term .of that equation, with the sign changed.' 2. The sum of the products of every two of the roots, is equal to the coefficient... | |
 | George Roberts Perkins - 1842 - 370 pages
...Now, by Art. 249, we know that the sum of the three roots of a cubic equation with their signs changed is equal to the coefficient of the second term of that equation ; and the sum of their products taken two and two, is equal to the coefficient of the third term ;... | |
 | Elias Loomis - 1846 - 380 pages
...the sum of all the roots with their signs changed. 2. The coefficient of the third term is equal to the sum of the products of all the roots taken two and two. 3. The coefficient of the fourth term is equal to the sum of the products of all the roots taken three... | |
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... is equal to the coefficient of the second term of that equation, with its sign changed. 
