 | Bewick Bridge - 1821 - 648 σελίδες
...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.... | |
 | British Association for the Advancement of Science - 1834 - 562 σελίδες
...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... | |
 | British Association for the Advancement of Science - 1834 - 564 σελίδες
...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... | |
 | Charles William Hackley - 1834 - 38 σελίδες
...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... | |
 | 1836 - 366 σελίδες
...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 —... | |
 | Ormsby MacKnight Mitchel - 1845 - 308 σελίδες
...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.... | |
 | Charles William Hackley - 1846 - 544 σελίδες
...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*... | |
 | Royal University of Ireland - 1859 - 490 σελίδες
...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... | |
 | Isaac Todhunter - 1861 - 330 σελίδες
...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... | |
 | Joseph Wolstenholme - 1867 - 368 σελίδες
...= 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"~'... | |
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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... 
