An Introduction to the Modern Theory of Equations
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In our eReader you can find the full English version of the book. Read An Introduction to the Modern Theory of Equations 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 Modern Theory of Equations
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There are 12 primitive roots. We have a;2i _ 1 = (x' - l)(x" + x7 + 1).
The roots of x' — 1 = are non-primitive for x^^ — 1 = 0. Since x' — 1 is a factor of x^^ — 1, tlie two primitive roots of x^ — 1 = are the two remaining non-primitive roots of x''' — 1 = 0. These two roots are roots of x2 4- a; + 1 = 0. Hence (x" -I- x'' -I- 1) -=- (x^ -|- x -1- 1) = is the re- quired equation. This is a reciprocal equation which can be depressed tox8-x6-6x*-l-6x3-f-8x2-8x-l-l=0.
Ex. 14. If — V— 1 is a prim...itive root of x" - 1 = 0, find n. If — V— 1 is a non-primitive root, what values may n take ?
CHAPTER VII SYMMETRIC FUNCTIONS OF THE ROOTS 68. Newton's Formulae for Sums of Powers of Roots. The sums of like powers of the roots of f(x) = can he expressed rationally in terms of the coefficients. The sum of the pth powers of the roots a, ji, y, 8, •■• of the equation f(x) = constitutes a symmetric function of the roots. The defini- tion and elementary discussion of symmetric functions were given in § 15.
What to read after An Introduction to the Modern Theory of Equations?
You can find similar books in the "Read Also" column, or choose other free books by Florian Cajori to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
There are 12 primitive roots. We have a;2i _ 1 = (x' - l)(x" + x7 + 1).
The roots of x' — 1 = are non-primitive for x^^ — 1 = 0. Since x' — 1 is a factor of x^^ — 1, tlie two primitive roots of x^ — 1 = are the two remaining non-primitive roots of x''' — 1 = 0. These two roots are roots of x2 4- a; + 1 = 0. Hence (x" -I- x'' -I- 1) -=- (x^ -|- x -1- 1) = is the re- quired equation. This is a reciprocal equation which can be depressed tox8-x6-6x*-l-6x3-f-8x2-8x-l-l=0.
Ex. 14. If — V— 1 is a prim...itive root of x" - 1 = 0, find n. If — V— 1 is a non-primitive root, what values may n take ?
CHAPTER VII SYMMETRIC FUNCTIONS OF THE ROOTS 68. Newton's Formulae for Sums of Powers of Roots. The sums of like powers of the roots of f(x) = can he expressed rationally in terms of the coefficients. The sum of the pth powers of the roots a, ji, y, 8, •■• of the equation f(x) = constitutes a symmetric function of the roots. The defini- tion and elementary discussion of symmetric functions were given in § 15.
What to read after An Introduction to the Modern Theory of Equations?
You can find similar books in the "Read Also" column, or choose other free books by Florian Cajori to read onlineMoreLess
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