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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
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - 1852 - 408 pages
...equation is wanting , the sum of the roots is equal to 0. 3. If the 3rd term of any equation is wanting, the sum of the products of the roots, taken two and two in a product, is equal to 0. 4. If the absolute term is wanting, the product of the roots must be 0,...
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A Treatise on Algebra

Elias Loomis - 1855 - 356 pages
...to 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=11. The last term is the product of all the roots (1X2X3) with their signs changed....
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A Treatise on Algebra

Benedict Sestini - 1857 - 258 pages
...with regard to the equations 0, . . . = 0, we will have x — t The coefficient B in [e] is equal to the sum of the products of the roots, taken two and two. If we suppose one of the roots wanting, for instance A, the products of the remaining roots, taken...
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A Treatise on Algebra

Elias Loomis - 1864 - 386 pages
...to 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=11. Ex. 2. Form the equation whose roots are 2, 3, 5, and —6. Ans. x ' —4.K'—29x'+156x—...
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A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - 1866 - 426 pages
...second term is the sum of all the roots, with their signs changed. The coefficient of the third term is the sum of the products of the roots, taken two and two, with their signs changed. The coefficient of the fourth term is the sum of the products of the roots,...
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Elements of Algebra: For Colleges, Schools, and Private Students, Book 2

Joseph Ray - 1866 - 420 pages
...coefficient is 0. U. If the 2J term is wanting, the sum of the roots is 0. III. If /lie 3d term is wanting, the sum of the products of the roots, taken two and two in a product, is 0. IV. If the absolute term is wanting, the product of the roots must be 0, and hence...
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Elements of algebra

Robert Wallace - 1870 - 164 pages
...coefficient of x"— ' is the sum of the roots taken with a negative sign ; the coefficient of x"—- is the sum of the products of the roots taken two and two ; the coefficient of x"—3 is the negative of the sum of the products of the roots taken three and...
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The Complete Algebra: Designed for Use in Schools, Academies, and Colleges

Joseph Ficklin - 1874 - 446 pages
...changed is equal lo the sum of the roots (592, 15, 1C) ; 2. The coefficient of the third term is equal to the sum of the products of the roots, taken two and two ; 3. T7ie coefficient of the fourth term with its sign changed is equal to the sum of the products...
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The Universal Solution for Numerical and Literal Equations: By which the ...

Michael Angelo McGinnis - 1899 - 207 pages
...again. 331. The coefficients of the second term of the sixth, like all other equations, represents the sum of the products of the roots, taken two and two. These combinations will form five cubic equations, as follows : x3 + (ab + cd + ef) x2 + (abed + dbef+...
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An Elementary Treatise on the Theory of Equations

Samuel Marx Barton - 1899 - 224 pages
...«4"- — «„; that is, the sum of the roots with their signs changed ; the coefficient of x"~- is the sum of the products of the roots taken two and two ; the coefficient of x"~3 is the sum of the products of the roots taken three at a time, with their...
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