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Books Books 1 - 10 of 29 on 3 of the fourth term, with its sign changed, is equal to the sum of the products....
" 3 of the fourth term, with its sign changed, is equal to the sum of the products of the roots taken three by three; and so on, the signs of the coefficients being taken alternately negative and positive, and the number of roots "
An Introduction to the Modern Theory of Equations - Page 11
by Florian Cajori - 1904 - 239 pages
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A General History of Mathematics from the Earliest Times to the Middle of ...

Charles Bossut - Astronomy - 1803 - 540 pages
...third is the sum of the products of the roots taken two fcy two: that the coefficient of the fourth is the sum of the products of the roots taken three by three with contrary signs ; and so on, to the last term, which is the product of all the roots taken with...
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The Elements of Algebra: Designed for the Use of Students in the University

John Hind - Algebra - 1837 - 539 pages
...q = 0, is manifestly equivalent to a; 2 - (a +/3) # + a/3 = 0: where the coefficient of the second term, with its sign changed, is equal to the sum of the roots, and the third term is equal to their product. 144. COK. 3. Since a? 2 - (a + /3) a? + a/3 =...
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An elementary treatise on the theory of equations

Isaac Todhunter - Equations, Theory of - 1861 - 279 pages
...coefficient of the third term is equal to the sum of the products of every two of the roots ; the coefficient of the fourth term with its sign changed is equal to the sum of the products of every three of the roots ; and so on. Thus generally if p r denote as usual the coefficient...
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A mathematical course for the University of London. (2nd)

Thomas Kimber - Mathematics - 1865 - 192 pages
...0, Or x* — (a + ft) x + a 0 = 0. 6 and id 0 Whence it appears that the coefficient of the second term, with its sign changed, is equal to the sum of the roots, and the third term is equal to their product. 183. Every equation of the form, x*" + p x" =...
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ELEMENTS OF ALGEBRA ON THE BASIS OF M. BOURDON: ENERACING

CHARLES DAVIES, LL.D. - 1871
...is equal to the sum of the different products of the roots, taken two in a set. 3d. The co-efficient of the fourth term, with its sign changed, is equal to the sum of the different products of the roots, taken three in a set, and so on. 4th. The absolute term, with its...
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The Complete Algebra: Designed for Use in Schools, Academies, and Colleges

Joseph Ficklin - Algebra - 1874 - 418 pages
...of the roots, taken two and tioo; 2 4 1—1 + 2 I +1 + 4 — 2 — 2 + 4 — 8 3. Tlie coefficient of the fourth term with its sign changed is equal to the sum of the products of the roots,taken three and three; and so on. 4. If the degree of the equation is even, the absolute term...
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A mathematical course for the University of London. (2nd)

1874
...) (x - p) = 0, Or x* — (a + /?) x + a $ = 0. Whence it appears that the coefficient of the second term, with its sign changed, is equal to the sum of the roots, and the third term is equal to their product. 188. Every equation of the form, x*™ + px m...
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An Elementary Treatise on the Theory of Equations

Isaac Todhunter - Equations, Theory of - 1880 - 328 pages
...coefficient of the third term is equal to the sum of the products of every two of the roots; the coefficient of the fourth term with its sign changed is equal to the sum of the products of every three of the roots; and so on. Thus generally if p r denote as usual the coefficient...
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THE THEORY OF EQUATIONS: WITH AN INTRODUCITON TO THE THEORY OF BINARY ...

WILLIAM SNOW BURNSIDE, M.A - 1881
...the third term is equal to the mm of the products of the roots taken two by two. The coefficient p^ of the fourth term with its sign changed is equal...alternately negative and positive, and the number of roots multiplied to g ether in each term of the corresponding function of the roots increasing by unity,...
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The Theory of Equations: With an Introduction to the Theory of Binary ...

William Snow Burnside, Arthur William Panton - Determinants - 1881 - 387 pages
...the third term is equal to the sum of the products of the roots taken two by two. The coefficient p 3 of the fourth term with its sign changed is equal...coefficients being taken alternately negative and posit ii'c, and the number of roots muffipfifd together in each term of the corresponding function...
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