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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. "
The Doctrine of Chances: Or, a Method of Calculating the Probabilities of ... - Page 226
by Abraham de Moivre - 1756 - 348 pages
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - 1811 - 404 pages
...second term if b — a + 2c = 0, or a — b = 2c. Cor. 3. An equation will want its third term, if the sum -of the products of the roots taken two and two, is partly positive, partly negative, and these mutually destroy each other. Remark. An incomplete equation...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 2

Charles Hutton - 1812 - 624 pages
...the second term if b — a + 2c = 0, or a—b =. 2c. Cor. 3. An equation will want its third term, if the sum of the products of the roots taken two and two, is partly positive, partly negative, and these mutually destroy each other. Remark. An incowfilefe...
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Elements of Geometry

Adrien Marie Legendre - 1819 - 574 pages
...taken with the contrary sign* will be the sum of the roots ; The coefficient of the third term will be the sum of the products of the roots, taken two and two ; The coefficient of the fourth term, ta],en with the contrary sign, will be the sum of the products...
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A Course of Mathematics for the Use of Academies, as Well as Private Tuition

Charles Hutton - 1822 - 680 pages
...second term if b — a -f 2c = 0, or arb ••= 2c. Cor. 3. An equation will want its third term, if the sum of the products of the roots taken two and two, is partly positive, partly negative * and these mutually destroy each other. Remark* --.Ant incomplete...
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Elements of Algebra

Silvestre François Lacroix - 1825 - 324 pages
...taken with the contrary sign, will be the sum of the roots ; The coefficient of the third term will be the sum of the products of the roots, taken two and two ; The coefficient of the fourth term, taken with the contrary sign, will be the sum of the products...
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Elements of Algebra: Tr. from the French of M. Bourdon, for the ..., Volume 1

Bourdon (M., Louis Pierre Marie) - 1831 - 446 pages
...the roots themselves, is equal to the coefficient 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 coefficient of the third term. 3d. The sum of the products...
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Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ...

Charles Davies - 1835 - 378 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. The sum of the products...
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Elements of Algebra

1838 - 372 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. The sum of the products...
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Lecture on the History of Mathematics

Francis Henney Smith - 1841 - 46 pages
...successive formation of the co-efficients of an equation, from the comInflation of the sum of its roots, the sum of the products of the roots, taken two and two, three and three, &c. He appears to have been the first who understood the use of negative roots, and...
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Elements of Algebra

Charles Davies - 1842 - 368 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. The sum of the products...
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