| Charles de Neuvéglise - 1700
...; 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
...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
...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 - 1831 - عدد الصفحات: 316
...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 - 1832 - عدد الصفحات: 352
...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
...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... | |
| 1836
...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 - 1837 - عدد الصفحات: 539
...+ 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 - 1837
...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
...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... | |
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