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

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 \dots ?

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