Sec Math teachers: I need a super powerful equation solver

[booklooker]

Any suggestions?

I want to solve x4-x3-x^2-x-1=0

But I need exact solutions (i.e. in surd form) Wolfram is good for cubics, but only gives to 4 s.f. for anything of higher degree.

Help me!

[MrsHerculePoirot]

It has exact solutions in Wolfram if you click exact solutions in the box where you get the answer to 4 sf...

[booklooker]

Thanks for that MrsHercule, I did try that following your suggestion, but still got the answer to 4 s.f.

It may well be because there is no way to solve a quartic analytically, so numerical solutions are sought instead.

[MrsHerculePoirot]

I did it using your equation and it worked! Let me see if I can post a link....

[MrsHerculePoirot]

www.wolframalpha.com/widgets/view.jsp?id=dcc8007e03af36a0bd3635b09e4cd5a2

[MrsHerculePoirot]

When I click exact solutions I get two horrific surd form solutions... But they are in exact form!

[booklooker]

Thank you so much MrsH, I really appreciate you making the effort on my behalf.

Let me put some context into my request.

The ratio between consecutive terms of the conventional Fibonacci sequence tends towards the solution to x^2-x-1=0

I noticed yesterday that the ratio for consecutive terms of sequence based upon adding the 3 previous terms tended towards the (real) solution of the equation x3-x2-x-1=0

And the (positive, real) ratio for a sequence adding up previous 4 terms tended towards the solution to x4-x3-x^2-x-1=0

I have been hunting for a pattern that can be generalised.