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Libros Libros 1 a 10 de 50 sobre These criteria were derived by a new transformation, namely the one which yields...
" These criteria were derived by a new transformation, namely the one which yields an equation whose roots are the squares of the differences of the roots of the given... "
A Treatise on the Stability of a Given State of Motion: Particularly Steady ... - Página 12
de Edward John Routh - 1877 - 108 páginas
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A Treatise on the Elements of Algebra

Bewick Bridge - 1821 - 227 páginas
...whether an equation Contains impossible roots. The method of detecting roots of this kind by means of the equation whose roots are the squares of the differences of the roots of the given equation, has been omitted on account of the difficulty attending the II • .if the transformation....
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A Synopsis of the Principal Formulae and Results of Pure Mathematics

Charles Brooke - 1829 - 358 páginas
...Bour. 303, 8.) THE EauATioN OF DIFFERENCES. (39.) Let/ + ft,-!/-1 + br_tf-°~ + ... + Ъ1у + Ь = Obe the equation whose roots are the squares of the differences of the roots of ф(а>) = 0, and cr,, <r2, &c. the sums of the 1st, 2nd, &c. powers of its roots. ^__ С* С* С* О...
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Report of the ... Meeting of the British Association for the ..., Número 3

British Association for the Advancement of Science - 1834
...determining the value of A. Waring first, and subsequently Lagrange, proposed for this purpose the formation of the equation whose roots are the squares of the differences of the roots of the given equation. If we subsequently transform this equation into one whose roots are the reciprocals...
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Report

British Association for the Advancement of Science - 1834
...determining the value of A. Waring first, and subsequently Lagrange, proposed for this purpose the formation of the equation whose roots are the squares of the differences of the roots of the given equation. If we subsequently transform this equation into one whose roots are the reciprocals...
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A catechism and notes upon the algebras of Bourdon and Lacroix: for the use ...

Charles William Hackley - 1834 - 26 páginas
...approximation ? 350. 218. When the roots differ by less than unity, how are they found ? Ans. Find the equation whose roots are the squares of the differences of the roots of the given equation ; then find the least limit to the roots of this equation ; suppose ^ to be this...
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Mathematical problems and examples, arranged according to subjects, from the ...

1836
...real roots. 84. Take away the third term from the equation a;4 — l8x3 — 6Qx2 + x — 2 = 0. Find the equation whose roots are the squares of the differences of the roots of the equation x3 + qx + r = 0. 85. The equation x3 — qa? + r = 0 has two impossible TO^ roots if —...
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An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - 1845 - 294 páginas
...resume the equation, If we make y2=z, and substitute, we obtain ^ z? — 42r!+441z— 49=0. This is an equation whose roots are the squares of the differences of the roots of the primitive equation, since *=y2. Let us now find the least limit to the roots of this equation....
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - 1846 - 503 páginas
...give the most simple and elegant solution of which it is susceptible. The question is this : To find the equation whose roots are the squares of the differences of the roots of a given equation, xm+Px™-'+Q:rm-iH ----- =0 . ....... [A] Represent the transformed equation by z»+pz»-l+qz''-*+rz*...
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The Queen's [afterw.] Royal university of Ireland calendar

1859
...and area of a spherical triangle, find the locus of its vertex. 3. Describe the method of forming an equation whose roots are the squares of the differences of the roots of a given equation. 4. How would you calculate the present value of an annuity on two joint lives to...
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An elementary treatise on the theory of equations

Isaac Todhunter - 1861 - 279 páginas
...= 0, and may therefore be calculated. 255. In Art. 1 09 we have explained one use which we may make of the equation whose roots are the squares of the differences of the situation of the real roots of the proposed equation. But Sturm's theorem now answers this purpose...
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