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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.
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 164
by Charles Hutton - 1811

## 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...

## 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...

## 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...

## 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...

## 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...

## Elements of Algebra: Including Sturms' Theorem

Charles Davies - 1845 - 382 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. 3d. The sum of the products...

## An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - 1845 - 308 pages
...d ..... &c ...... — /; or, the sum of the roots, with the contrary sign, Q,=ab+ac+ad+bc+bd+, &c.; the sum of the products of the roots, taken two and two, R= — abc-\-abd-\-, &c.; the sum of the products of the roots, taken three and three, with the contrary...

## A Treatise on Algebra

Elias Loomis - 1846 - 380 pages
...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. The last term k" the product of all the roots (1X2x3) with their signs changed....