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" In every algebraic equation, the coefficient of whose highest term is unity, the coefficient pi of the second term with its sign changed is equal to the sum of the roots. The coefficient... "
A College Algebra - Page 427
by Henry Burchard Fine - 1904 - 595 pages
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The Elements of Algebra: Designed for the Use of Students in the University

John Hind - Algebra - 1837 - 539 pages
...a?2 - pas + q = 0, is manifestly equivalent to a?8 - (a + )8) a? + 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. Con. 3. Since a? (a + ft) tv + a/3...
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NEW COMBINATIONS Binomial Cheorem and Logorithuis;

JOSEPH B. MOTT. - 1855
...af+AVl~1+BVi-2+CVl-3+&;c. to (last coefficient) xn~n = 0, is such, 1, that the coefficient of the second term (A'), with its sign changed, is equal to the sum of all the roots. 2 That the coefficient of the third term (B') is equal to the sum of all the products that can be...
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ENUMERATION OF LINES OF THE THIRD ORDER

C.R. M. TALBOT - 1860
...let ^(aa: + b)yn~1 + (ca;* + da: + e)yn~*'-' &c. = o Then, since in every equation the coefficient of the second term with its sign changed is equal to the excess by which the sum of the positive exceeds the sum of the negative roots, where this term is deficient,...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies, Bourdon (M., Louis Pierre Marie) - Algebra - 1860 - 400 pages
...the following conclusions with reference to the values of the co-efficients : 1st. The co-efficient of the second term, with its sign changed, is equal to the algebraic sum of the roots of the equation. 2d. The co-efficient of the third term is equal to the...
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An elementary treatise on the theory of equations

Isaac Todhunter - 1861
...product of all the roots with their signs changed. Or we may enunciate the laws thus : the coefficient of the second term with its sign changed is equal to the sum of the roots ; the coefficient of the third term is equal to the sum of the products of every two of the...
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A mathematical course for the University of London. (2nd)

Thomas Kimber - 1865
...0, (х - a) (,r - /8) = 0, Or я* (a + /3) 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. 183. Every equation of the form, x'm + p xm...
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ELEMENTS OF ALGEBRA ON THE BASIS OF M. BOURDON: ENERACING

CHARLES DAVIES, LL.D. - 1871
...the following conclusions with reference to the values of the co-efficients : 1st. The co-efficient of the second term, with its sign changed, is equal to the algebraic sum of the roots of the equation. 2d. The co-efficient of the third term is equal to the...
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An Elementary Treatise on the Theory of Equations: With a Collection of Examples

Isaac Todhunter - Algebra - 1875 - 328 pages
...product of all the roots with their signs changed. Or we may enunciate the laws thus : the coefficient of the second term with its sign changed is equal to the sum of the roots ; the coefficient of the third term is equal to the sum of the products of every two of the...
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The Theory of Equations: With an Introduction to the Theory of Binary ...

William Snow Burnside, Arthur William Panton - Binary system (Mathematics) - 1886 - 448 pages
... In every algebraic equation, the coefficient oj trhose highest term is unity, the coefficient pi of the second term with its sign changed is equal to the sum of the roots. The coefficient p2 of the third term is equal to the sum of the products of the roots taken...
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The theory of equations: with an introduction to the theory of binary ...

William Snow Burnside, Arthur William Panton - Determinants - 1886 - 448 pages
... In every algebraic equation, the coefficient of ichose highest term is unity, the coefficient pi of the second term with its sign changed is equal to the sum of the roots. The coefficient p2 of the third term is equal to the sum of the products of the roots taken...
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