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 444by Henry Burchard Fine - 1904 - 595 pagesFull view - About this book
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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.... | |
| 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 — ß, x — y, etc., corresponding... | |
| 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, x—c, etc., corresponding... | |
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