 | Charles de Neuvéglise - Mathematics - 1700 - 1254 pages
...; for from the algebraical Expreffions of the Quantities and the binomial Theorem, it appears that the Coefficient of the third Term is the Sum of the Products of the Roots, taken two by iwo ; whence its Square is equal to the Sum of the Squares of the Produâs... | |
 | C T. Watkins - 1810 - 1056 pages
...The coefficient of Ihc first term is f. The rocmcitnt of the second term is the sum of ihe гном with their signs changed. The coefficient of the third term is the sum ot all the products made by multiplying iiny two of the roots together, 1 he свешаем of the... | |
 | L. Murray - 1821 - 620 pages
...equation. 2. The coefficient of the first term is 1. The coefficient of the second term is the sum of tiie roots with their signs changed. The coefficient of the third term is the sum of all the products made by multiplying any two of the roots together. The coefficient of the fourth term... | |
 | Peter Nicholson - Algebra - 1831 - 326 pages
...term, are the second terms or parts of the binomial factors, of •which the equation is the product ; the coefficient of the third term is the sum of the products of every two of these second parts, the coefficient of the fourth term is the sum of the products of every three... | |
 | John Radford Young - Algebra - 1832 - 408 pages
...and negative roots*. PROPOSITION v. The coefficient of the second term in any equation is equal to the sum of the roots with their signs changed ; the coefficient of the third term is equal to the sum of the products of every two roots with their signs changed ; the coefficient of the... | |
 | John Radford Young - 1835 - 302 pages
...term, or highest power of x, has the coefficient unity, the coefficient of the second term is equal to the sum of the roots with their signs changed; the coefficient of the third term is equal to the sum of the products of every two roots with their signs changed ; the coefficient of the... | |
 | Mathematics - 1836 - 366 pages
...one positive, the other negative. 66. The coefficient of the second term of an equation, with 1833 its proper sign, is the sum of the roots with their...products of every two roots with their signs changed, &c., and the last term is the product of all the roots with their signs changed. 67. Find a number... | |
 | John Hind - Algebra - 1837 - 584 pages
...+ ac + be) a; - abc = 0. Hence, conversely as in article (143), the coefficient of the second term, with its proper sign, is the sum of the roots with...products of every two roots with their signs changed, and the coefficient of the last term is the product of all the roots with their signs changed. Similar... | |
 | James Bryce - Algebra - 1837 - 322 pages
...with its sign changed ; the coefficient of the second term is their sum with its sign changed, and the coefficient of the third term is the sum of the products of the roots taken by pairs ; and the same holds true of every cubic equation, with whatever signs the... | |
 | John Radford Young - 1839 - 332 pages
...change, and one positive PROPOSITION V. The coefficient of the second term in any equation is equal to the sum of the roots with their signs changed ; the coefficient of the third term is equal to the sum of the products of every two roots with their signs changed ; the coefficient of the... | |
| |
In any equation in its simplest form the coefficient of the second term is equal to the sum of the roots with their signs changed ; the coefficient of the third term is... 
