# Talk

## Sec Math teachers: I need a super powerful equation solver

(7 Posts)
booklooker Sat 03-Sep-16 10:58:04

Any suggestions?

I want to solve x^4-x^3-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!

Sat 03-Sep-16 11:01:52

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

booklooker Sat 03-Sep-16 12:09:45

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.

Sat 03-Sep-16 15:33:19

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

Sat 03-Sep-16 15:37:20
Sat 03-Sep-16 15:39:08

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

booklooker Sat 03-Sep-16 18:21:39

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 x^3-x^2-x-1=0

And the (positive, real) ratio for a sequence adding up previous 4 terms tended towards the solution to x^4-x^3-x^2-x-1=0

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

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