solved the general quintic, despite whatever proof that it cant be solved in a simple way!


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Question Number 66302 by ajfour last updated on 12/Aug/19

$s o l v e d t h e g e n e r a l q u i n t i c,$ $d e s p i t e w h a t e v e r p r o o f t h a t i t$ $c a n t b e s o l v e d i n a s i m p l e w a y!$
Commented by mr W last updated on 12/Aug/19

$i k n e w {y o u}^{'} l l t e l l u s t h e g o o d n e w s .$ $t h a n k s s i r!$
Commented by ajfour last updated on 12/Aug/19

$i {h a v e n}^{'} t v e r i f i e d i t y e t, b u t i$ $t h i n k t h e m e t h o d i s t o o l e n g t h y$ $b u t p l a u s i b l e!$ $S i r c o n s i d e r$ $t^{5} + {a t}^{3} + {b t}^{2} + c t + d = 0$ $c a n o n e r o o t b e i n d e p e n d e n t o f$ $t h e c o n s t a n t t e r m d ?$
Commented by MJS last updated on 12/Aug/19

$you know that$ $\underset{i = 1}{\prod^{n}} (x - α_{i})$ $leads to the constant term$ ${(- 1)}^{n} \underset{i = 1}{\prod^{n}} α_{i}$ $\Rightarrow the constant factor depends on the roots$ $and vice versa . this is obvious, or . . . ?$
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