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" Suppose now a polynomial formed of the product of the factors corresponding to the negative and imaginary roots of an equation ; the effect of multiplying this by each of the factors x - a, x... "
A College Algebra - Page 444
by Henry Burchard Fine - 1904 - 595 pages
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An elementary treatise on the theory of equations

Isaac Todhunter - 1861
...of sign in the new polynomial than in the original polynomial. If then we suppose the product of all the factors corresponding to the negative and imaginary roots of an equation already formed, by multiplying by the factor corresponding to each positive root we introduce at least...
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An Elementary Treatise on the Theory of Equations: With a Collection of Examples

Isaac Todhunter - Algebra - 1875 - 328 pages
...of sign in the new polynomial than in the original polynomial. If then we suppose the product of all the factors corresponding to the negative and imaginary roots of an equation already formed, by multiplying by the factor corresponding to each positive root we introduce at least...
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THE THEORY OF EQUATIONS: WITH AN INTRODUCITON TO THE THEORY OF BINARY ...

WILLIAM SNOW BURNSIDE, M.A - 1881
...factor x - a is to introduce at least one additional change of sign. Suppose now a polynomial formed of the product of the factors corresponding to the negative and imaginary roots of an equation.; the effect of multiplying this by each of the factors x - a, x -j3, #--7, &c., corresponding to the...
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An Elementary Treatise on the Theory of Equations with a Collection of Examples

Isaac Todhunter - Equations, Theory of - 1882 - 328 pages
...of sign in the new polynomial than in the original polynomial. If then we suppose the product of all the factors corresponding to the negative and imaginary roots of an equation already formed, by multiplying by the factor corresponding to each positive root we introduce at least...
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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
...x - a is to introduce at least one additional change of I sign. Suppose now a polynomial formed of the product of the factors corresponding to the negative and imaginary roots of an equation ; the effect of multiplying this by each of the factors x - a, x - |3, x - y, &c., corresponding to...
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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
...factor x - a is to introduce at least one additional change of sign. Suppose now a polynomial formed of the product of the Factors corresponding to the negative and imaginary roots of an equation ; the effect of multiplying this by each of the factors t - a, x -,/3, x - -y, &c., corresponding to...
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A Short Course in Higher Algebra: For Academies, High Schools, and Colleges

Webster Wells - Algebra - 1889 - 478 pages
...increases the number of variations in the equation by at least one. If, then, we form the product of all the factors corresponding to the negative and imaginary roots of an equation, multiplying the result by the factor corresponding to each positive root introduces at least one variation....
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College Algebra

Webster Wells - Algebra - 1890 - 577 pages
...corresponds' one in (2), and besides the last term of (2) is dotted. If, then, we form the product of ail the factors corresponding to the negative and imaginary roots of an equation, multiplying the result by the factor corresponding to each positive root introduces at least one variation....
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An Elementary Treatise on the Theory of Equations

Samuel Marx Barton - Equations, Theory of - 1899 - 199 pages
...binomial x a is to introduce at least one change of sign. Now suppose we have a polynomial formed of the product of the factors corresponding to the negative and imaginary roots of an equation. The effect of multiplying this by each of the factors x a, x , x y, etc., corresponding...
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College algebra

James Harrington Boyd - Algebra - 1901 - 777 pages
...original polynomial excepting a change of signs at the end. Suppose now that a polynomial is formed of the factors corresponding to the negative and imaginary roots of an equation; the result of multiplying this product by each of the factors x a, x b, xc, etc., corresponding...
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