 | 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 - 422 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 - 754 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... | |
 | 1897 - 672 pages
...that a simple equation has one root, and a quadratic equation has two roots. In general, any equation has as many roots as there are units in the exponent of the unknown quantity. EXAMPLE. — Solve the equation '-- — '- — jp~ = jg-. SOLUTION. — Clearing... | |
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... and — . The preceding equation is only of the fourth power or degree ; but it is manifest that the above remark applies to equations of higher or lower dimensions : viz, that in general . an equation of any degree whatever has as many roots as there... 
