Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" 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 Synopsis of the Principal Formulae and Results of Pure Mathematics - Page 46
by Charles Brooke - 1829 - 358 pages
Full view - About this book

A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1821 - 648 pages
...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....
Full view - About this book

Report of the Annual Meeting, Issue 3

British Association for the Advancement of Science - Science - 1834 - 562 pages
...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...
Full view - About this book

Report of the ... Meeting of the British Association for the ..., Volume 3

British Association for the Advancement of Science - Science - 1834 - 564 pages
...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...
Full view - About this book

A Catechism and Notes Upon the Algebras of Bourbon and Lacroix: For the Use ...

Charles William Hackley - Algebra - 1834 - 38 pages
...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...
Full view - About this book

Mathematical Problems and Examples, Arranged According to Subjects, from the ...

Mathematics - 1836 - 366 pages
...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 —...
Full view - About this book

An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...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....
Full view - About this book

A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1846 - 544 pages
...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*...
Full view - About this book

The Calendar for the Year ...

Royal University of Ireland - Universities and colleges - 1859 - 490 pages
...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...
Full view - About this book

An elementary treatise on the theory of equations

Isaac Todhunter - Equations, Theory of - 1861 - 330 pages
...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...
Full view - About this book

A Book of Mathematical Problems on Subjects Included in the Cambridge Course

Joseph Wolstenholme - Mathematics - 1867 - 368 pages
...= 0. 911. Find the sum of the wth powers of the roots of the equation x' — 3? + 1 = 0 ; and form the equation whose roots are the squares of the differences of the roots of the given equation. 912. If sr denote the sum of the rth powers of the roots of the equation x" +plx"~'...
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF