Contribution on radical solution of higher degree general polynomia
Equations and number theory - Part one
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This book is a collection of works by the author in search for radical solution of general polynomial equations of degree five and above. The work of Abel (1824) and Galois showed that radical solutions of such higher degree polynomial equations are impossible. The impossibilities are however mainly due to the approaches used in seeking the solution of these higher degree polynomial equations. The Lagrange and Galois resolvents succeed in solving cubic and quartic equations. They fail to obtain radical solutions of higher degree general polynomial equations. These solutions are however possibl...
This book is a collection of works by the author in search for radical solution of general polynomial equations of degree five and above. The work of Abel (1824) and Galois showed that radical solutions of such higher degree polynomial equations are impossible. The impossibilities are however mainly due to the approaches used in seeking the solution of these higher degree polynomial equations. The Lagrange and Galois resolvents succeed in solving cubic and quartic equations. They fail to obtain radical solutions of higher degree general polynomial equations. These solutions are however possible through careful search of solvable factorized forms. The unknown coefficients of these factorized forms are then solved to obtain their rational or radical solution in terms of the original coefficients before solving the auxiliary equations. The book is a simple presentation of how radical solutions can be obtained by methods of factorization. The solution methods prescribed in it do not required knowledge of abstract algebra or even Galois theory. The only basic prerequisites needed is ability to understand solution methods of cubic and quartic equations.
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