quartic equation
in [Math]
|
Prev: Decimal Expansion of 1/7 -
Next: Geometry question
From: kinor on 15 May 2010 20:15 How does one find all complex solutions to the equation x^4 - x^3 + x^2 - x + 1 = 0. Thanks. k
From: Ken Pledger on 15 May 2010 21:46 In article <49c00cae-e0ad-46d9-9ddc-3df38e6ce67f(a)u21g2000vbr.googlegroups.com>, kinor <kinor(a)excite.com> wrote: > How does one find all complex solutions to the equation > > x^4 - x^3 + x^2 - x + 1 = 0. > .... You may notice that the terms form a (finite) geometric series, so the formula for its sum should help. In fact what that amounts to is multiplying your equation by (x + 1) to get a 5th-degree equation which is easier to think about. Ken Pledger.
From: amzoti on 15 May 2010 22:49 On May 15, 5:15 pm, kinor <ki...(a)excite.com> wrote: > How does one find all complex solutions to the equation > > x^4 - x^3 + x^2 - x + 1 = 0. > > Thanks. > > k There was another post by KP that is worth exploring. What have you tried? Did you check out: http://mathforum.org/dr.math/faq/faq.cubic.equations.html
From: no comment on 15 May 2010 23:40 On May 15, 7:49 pm, amzoti <amz...(a)gmail.com> wrote: > On May 15, 5:15 pm, kinor <ki...(a)excite.com> wrote: > > > How does one find all complex solutions to the equation > > > x^4 - x^3 + x^2 - x + 1 = 0. > > > Thanks. > > > k > > There was another post by KP that is worth exploring. > > What have you tried? > > Did you check out:http://mathforum.org/dr.math/faq/faq.cubic.equations.html Hello, You may want to try the following. Divide by x^2. Then let u = x + 1/ x. After a little while you should be able to find a simple quadratic equation satisfied by u. And once you know the possible values of u, another simple quadratic equation leads will lead you to all solutions x.
From: William Elliot on 16 May 2010 02:46
On Sat, 15 May 2010, kinor wrote: > How does one find all complex solutions to the equation > > x^4 - x^3 + x^2 - x + 1 = 0. Hint. x^5 + 1 = (x + 1)(x^4 - x^3 + x^2 - x + 1) |