Solving a solvable quintic

evene · 2016-10-20 12:59:09

Is there a way to solve for the roots of the quantic

mostly by hand?

It should be solvable.

bobbym · 2016-10-20 13:27:48

Hi;

Mostly by hand? I do not think so. Root extraction other than for book problems is done with a computer.

Yuriy S wrote:

It also depends on what you need the solution for. If it's for practical purposes, the numerical methods are usually better (like the Newton's method) and they work for any polynomial equation.

Exacto Mundo!

1) Use a Cauchy bound to isolate the roots they are between {-22, 22}.

2) Graph the poly:

You can see 5 real roots and the graph can provide initial guesses for iterative scheme.

3) There are Sturm sequences, Descartes rule of signs, rational root theorem... How do you want to go?

evene · 2016-10-20 13:39:27

According to Wikipedia, the roots are equal to

So the rational root theorem won't work.

But I'm wondering if it's possible to compute it mostly by hand. Like, not get a computer software, plug in the polynomial and have the roots shown instantly.

I think this may have something to do with Galois Theory... but I'm not too sure.

Last edited by evene (2016-10-20 13:51:43)

bobbym · 2016-10-20 13:40:36

Can you adjust the latex so it is readable?

evene · 2016-10-20 13:41:51

Done!

Just learned that the double backslash \\ doesn't work to break the line. Is there an alternative way?

bobbym · 2016-10-20 13:43:56

My first question would be do you think that the guy who put that page together actually did those by hand?

Root extraction other than for book problems is done with a computer.

You have posted a book problem one of the five or six where that method will work.

There was someone in here that posted how he does the ones that are solveable by that method. I just can not remember who it was.

evene · 2016-10-20 13:53:15

Okay, can I say minimize? Like, if computation by hand is possible, then you do it by hand?

I just want to stay away from computers because I think that they don't really improve your mental math skills and encourage laziness! (For me at least)

bobbym · 2016-10-20 13:54:54

You can do that one by hand but the page does not seem to show how.

There was someone in here that posted how he does the ones that are solveable by that method. I just can not remember who it was.

Wait a minute, it was you that was posting about this very technique.

http://www.mathisfunforum.com/viewtopic … 10#p383510

Math Is Fun Forum

#1 2016-10-20 12:59:09

Solving a solvable quintic

#2 2016-10-20 13:27:48

Re: Solving a solvable quintic

#3 2016-10-20 13:39:27

Re: Solving a solvable quintic

#4 2016-10-20 13:40:36

Re: Solving a solvable quintic

#5 2016-10-20 13:41:51

Re: Solving a solvable quintic

#6 2016-10-20 13:43:56

Re: Solving a solvable quintic

#7 2016-10-20 13:53:15

Re: Solving a solvable quintic

#8 2016-10-20 13:54:54

Re: Solving a solvable quintic

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