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" ... 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 are units in... "
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 162
by Charles Hutton - 1811
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A Theoretical and Practical Treatise on Algebra ...

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...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

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....
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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

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....
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Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

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...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

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...
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New Higher Algebra: An Analytical Course Designed for High Schools ...

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...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

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...
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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

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....
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University Algebra

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....
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The Normal Teacher, Volume 3

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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