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 450by Henry Burchard Fine - 1904 - 595 pagesFull view - About this book
| Isaac Todhunter - Equations, Theory of - 1861 - 330 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... | |
| Isaac Todhunter - Algebra - 1875 - 344 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... | |
| William Snow Burnside, Arthur William Panton - Determinants - 1881 - 407 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 x - a, x -j3, #--7, &c., corresponding to the... | |
| Isaac Todhunter - Equations - 1882 - 348 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... | |
| William Snow Burnside, Arthur William Panton - Determinants - 1886 - 478 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... | |
| William Snow Burnside, Arthur William Panton - Determinants - 1886 - 480 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... | |
| Webster Wells - Algebra - 1889 - 584 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.... | |
| Webster Wells - Algebra - 1890 - 604 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.... | |
| Samuel Marx Barton - Determinants - 1899 - 224 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 — ß, x — y, etc., corresponding... | |
| James Harrington Boyd - Algebra - 1901 - 812 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, x—c, etc., corresponding... | |
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