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Bøker Bok 110 av 20... preceding equation is only of the fourth power or degree ; but it is manifest...
" ... 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 ...: Composed for the Use of the Royal Military ... - Side 174
av Charles Hutton - 1811
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The Elements of Mathematical Analysis: Abridged, for the Use of Students ...

Nicolas Vilant - 1798 - 170 sider
...all degrees to be produced by a multiplication of binomial factors. Every affefted equation will have as many roots as there are units in the exponent of the higheft power of the variable quantity ; and, if the terms of the equation are alternately affirmative...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volum 2

Charles Hutton - 1812
...that which characterizes these roots is, that on substituting each of them successively instead of x+ the aggregate of the terms of the equation vanishes...exponent of the highest power of the unknown quantity, und that each root has the properly of rendering, by its substitution in place of the unknown quantity,...
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Encyclopaedia Britannica; Or A Dictionary of Arts, Sciences, and ..., Volum 13

1823
...degree may be considered as proekiced by the multiplication of аз many simple equations ns there arc units in the exponent of the highest power of the unknown quantity. From this he deduced the relation which exists bctw en the roots of an equation, and the coefficients...
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A Course of Mathematics for the Use of Academies: As Well as ..., Volum 2

Charles Hutton - 1826
...four roots or values of x ; and that which characterizes these roots is, that on substituting eacb of them successively instead of r, the aggregate of...of the highest power of the unknown quantity, and thnt each root h;is the property of rendering, by its substitution in place of the unknown quantity,...
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A Course of Mathematics: For the Use of Academies as Well as Private Tuition ...

Charles Hutton - 1831
...aggregate of the terms of the equation vanishes, by the opposition of the signs + and — . ' 1 he preceding equation is only of the fourth power or...quantity, the aggregate of all the terms of the equation equul to nothing. It must be observed that we cannot have all at once x = a, x = b, x = c, &c. for...
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A Course of Mathematics: For the Use of Academies, as Well as ..., Volum 2

Charles Hutton - 1831
...is only of the fourth power or degree ; but it is manifest that the above remark applies i<equations of higher or lower dimensions : viz. that in general...rendering, by its substitution in place of the unknown quantify, the aggregate of all Ihe terms of the equation equal to nothing. It must be observed that...
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Elements of Algebra: Tr. from the French of M. Bourdon

Charles Davies - 1835 - 353 sider
...law should be remembered. Second Property. 264. Every equation involving but one unknown quantity, has as many roots as there are units in the exponent of its degree, and no more. Let the proposed equation be if+Par-i+Q«" 3+ • • . +Tx+\J=0. Since every...
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Elements of algebra

Bourdon (Louis Pierre Marie, M.) - 1838 - 355 sider
...law should be remembered. Second Property. 281. Every equation involving but one unknown quantity, has as many roots as there are units in the exponent of its degree, and no more. Let the proposed equation be xn+Pxm~l+Q.xm-2+ . . . +Ta;+U=0. Since every...
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The Analysis and Solution of Cubic and Biquadratic Equations: Forming a ...

John Radford Young - 1842 - 247 sider
...all arranged on one side, the polynomial we thus get is composed of as many simple binomial factors as there are units in the exponent of the highest power of the unknown quantity. The discovery of these factors would he the discovery of the roots of the equation, since these are...
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An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - 1845 - 294 sider
...on of the divisors of all degrees. 234. As an exemplification of the principle, that every equation has as many roots as there are units in the exponent of the highest power of the unknown quantity, we propose to examine the equation xm—! =0. Let us commence by making m=2, and we have x2 — 1=0By...
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