| Horatio Nelson Robinson - 1848 - 354 pages
...to 0, at the same time, the equation becomes x2-\-r=0, a binomial equation. Every binomial equation **has as many roots as there are units in the exponent of the** unknown quantity. Thus 0^+8=0, and a;»— 8=0, or r'+l=0, and a? — 1=0, &c., are equations which... | |
| Joseph Ray - 1852 - 408 pages
...and y«-8y =16; . Whence, y =8, or — 2. It will be shown hereafter, (Art. 396), that every equation **has as many roots as there are units in the exponent of the highest power of the unknown quantity.** We do not, therefore, by this method, in all cases, obtain all the values of the unknown quantity.... | |
| Joseph Ray - 1857 - 408 pages
...Therefore, x2=8, or — 2. and x =2, or — ij2. It will be shown hereafter, (Art. 396), that every equation **has as many roots as there are units in the exponent of the highest power of the unknown quantity.** We do not, therefore, by this method, in all cases, obtain all the values of the unknown quantity.... | |
| James B. Dodd - 1859 - 368 pages
...Number of Roots of an Equation. (255.) Every Equation containing but one unknown quantity, has just **as many roots as there are units in the exponent of the highest power of the unknown quantity** in the equation. Let a represent a root of the cubic Equation x3+mx2+nx=i. Transposing s to the first... | |
| Horatio Nelson Robinson - 1863 - 432 pages
...(l) to disappear. Prom this we might conclude that every equation involving but one unknown quantity, **has as many roots as there are units in the exponent of** its degree, and can have no more. •425. Admitting that every equation containing but one unknown... | |
| Benjamin Greenleaf - 1864 - 420 pages
...of x, it is evident that the original equation can be separated into as many such binomial factors **as there are units in the exponent of the highest power of the unknown quantity, and** no more ; that is, into n factors, or (x — a) (x — b) (x — c) ..... (x — I) = 0. Hence, by... | |
| Horatio Nelson Robinson - 1864 - 444 pages
...(1) to disappear. From this we might conclude that every equation involving but one unknown quantity, **has as many roots as there are units in the exponent of** its degree, and can have no more. 435. Admitting that every equation containing but one unknown quantity... | |
| Joseph Ray - 1852 - 420 pages
...2. and x =2, or — V3. It vrt- 1 be shown hereafter, (Art. 396), that every equation hag as mf'.iy **roots as there are units in the exponent of the highest power of the unknown quantity.** We do not, therefore, by thia method, in all cases, obtain all the values of the unknown quantity.... | |
| Webster Wells - 1879 - 468 pages
...of x, it is evident that the original equation can be separated into as many such binomial factors **as there are units in the exponent of the highest power of the unknown quantity, and** no more ; that is, into n factors, or (ж — a) (x — V) (x — c) (x — f) = Q. Hence, by Art.... | |
| 1880 - 718 pages
...equation also shows, that the number of roots in the first two equations is six; for every equation **has as many roots as there are units in the exponent of the highest power of the unknown quantity.** Now let us see how the curves of these two equations intersect each other, and how the roots determine... | |
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