Please elaborate .
-
-
-
For any polynomial of degree 4 or less, there is a formula to extract the roots in terms of radicals of the coefficients of the polynomial (e.g. the Quadratic Formula). However, for a general polynomial of degree 5 or higher, there is no such formula.
- 3 more replies
New conversation -
-
-
Wow. The complexity rises quickly. The solution to ax^3+bx^2+cx+d=0 is in the 1st picture (which I've never seen). One expects three solutions (here's one), Two solutions might be imaginary (2nd picture). https://math.vanderbilt.edu/schectex/courses/cubic/ ……pic.twitter.com/y3MhoaHxjz
-
Interestingly, in formulating and proving this equation, Rafael Bombelli, coined the value of "i" as a constant, in order to solve the inconsistency. Both "i"s would cancel itself, giving a numerical answer for x. He thought it was a pure coincidence and ignored his discovery.
- 1 more reply
New conversation -
-
-
And died in a duel next day!?
-
No, that was Galois, not Abel! Abel was murdered by Kain...

- 1 more reply
New conversation -
-
-
There also happens to be a non-algebraic closed formula for the roots of the quintic which uses modular forms and elliptic integrals:https://math.stackexchange.com/a/541027
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
So it is possible to solve up to degree 4?
-
Yes u can solve upto degree 4
End of conversation
New conversation -
-
-
There seems to be some confusion in the comments. This theorem does not imply that ALL quintics are unsolvable. For example (×-1)^5=0 is trivial to solve. It simply states that given an arbitrary a,b,c,d,e there is no solution in terms of radicals of those coefficients.
-
Thus this theorem really states that there are SOME quintics that can't be solved by radicals, like x^5-x-1 for example. Galois Theory specifies when polynomials are solvable by identifying their Galois Groups and determining if those groups are solvable.
End of conversation
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.