| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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 —... | |
| 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.... | |
| 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*... | |
| 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... | |
| 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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