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Solve x^4

  1. Apr 8, 2003 #1
    how to solve the x from x^4+x^3.....=...??
    i mean from the equation for x power of 4
    like the x^2-2x+1=0
    the solve are x=1,x=1
  2. jcsd
  3. Apr 8, 2003 #2

    eg. x^4 + x^2 = 0
    now y=x^2
    --> y^2 + y = 0

    you can solve this for y (= x^2)
  4. Apr 8, 2003 #3
    the full solution of the quartic equation is fairly long. so rather than retyping a lot of calculations, i will link you to a solution here
  5. Apr 8, 2003 #4
    Cutely, it's provable that you can't find a general solution (using addition/subtraction, multiplation/division, and roots) for polynomials in any order higher than quartic. The proof uses the same technique (Galois theory, loosely) as the geometric nom-constructibility proofs for things like trisecting an angle.
  6. Apr 8, 2003 #5
    How effective is the p/q method for finding roots of quartics or higher order polynomials? Remind me how it works for a simple example.
  7. Apr 9, 2003 #6
    what is the p/q method?

    the quartic solution is 100%. it is guaranteed to give you four exact analytic roots to your quartic.
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