An Introduction to the Algebra of Quantics
An Introduction to the Algebra of Quantics
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In our eReader you can find the full English version of the book. Read An Introduction to the Algebra of Quantics Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Introduction to the Algebra of Quantics
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Taking either root c' of this cubic we can solve the linear equations in II', Im' + l'm, mm', and so obtain their ratios, i. E. Obtain the product ll'x 2 + (lm' + l'm)xy + mm'y 2 of Ix + my, I'x + m'y but for a constant factor. /> 221. Solution of a quartic equation. When a quartic is reduced to its canonical form, or to the form a'x* + 6 cx z y z + e'y*, it is at once broken up into quadratic factors and solved. Two methods suggested by the articles which precede are here exemplified. They are... not so simple in their use as some of those given in works on the theory of equations.
Ex. 28. By use of 220 solve the quartic equation 3o; 4 -4ar J +24ce 2 -16a; + 48 = 0.
Here a, b, c, d, e have the values 3, 1, 4, 4, 48. Thus /= 176, J = 448, and the cubic for c' is c /3 -44c / +112 = 0, of which 4 is a root. The corresponding ratios IV : lm' + I'm : mm' of 220 are 1:0: 4. The quartic has then the form a" (x + 2) 4 + J' (x - 2) 4 + 6 c" (a; 2 - 4) 2 = 0, and is in fact seen to be . E. I. E. So that the roots are + 2 1 and i (2 + 4 1 \/2).
What to read after An Introduction to the Algebra of Quantics?
You can find similar books in the "Read Also" column, or choose other free books by E B Edwin Bailey Elliott to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Taking either root c' of this cubic we can solve the linear equations in II', Im' + l'm, mm', and so obtain their ratios, i. E. Obtain the product ll'x 2 + (lm' + l'm)xy + mm'y 2 of Ix + my, I'x + m'y but for a constant factor. /> 221. Solution of a quartic equation. When a quartic is reduced to its canonical form, or to the form a'x* + 6 cx z y z + e'y*, it is at once broken up into quadratic factors and solved. Two methods suggested by the articles which precede are here exemplified. They are... not so simple in their use as some of those given in works on the theory of equations.
Ex. 28. By use of 220 solve the quartic equation 3o; 4 -4ar J +24ce 2 -16a; + 48 = 0.
Here a, b, c, d, e have the values 3, 1, 4, 4, 48. Thus /= 176, J = 448, and the cubic for c' is c /3 -44c / +112 = 0, of which 4 is a root. The corresponding ratios IV : lm' + I'm : mm' of 220 are 1:0: 4. The quartic has then the form a" (x + 2) 4 + J' (x - 2) 4 + 6 c" (a; 2 - 4) 2 = 0, and is in fact seen to be . E. I. E. So that the roots are + 2 1 and i (2 + 4 1 \/2).
What to read after An Introduction to the Algebra of Quantics?
You can find similar books in the "Read Also" column, or choose other free books by E B Edwin Bailey Elliott to read onlineMoreLess
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