It has been known for a long time that there is no general analytical solution to determine zeros of quintics (polynomials of degree 5) by radical expressions. However certain classes of quintic equations can be solved including both reducible and irreducible cases.In this book a wide range of reducible quintics is analysed which can be linked to symmetric settings of zeroes. Specifically if there are two square roots or if more than two zeroes of a quintic equation are located in a circular sym
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