What is the p/q Method in Solving Quartic or Higher Order Polynomials?

[newton1]

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

 

[ottjes]

substitution

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

you can solve this for y (= x^2)

 

[lethe]

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

 

[damgo]

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.

 

[Loren Booda]

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.

 

[lethe]

Originally posted by Loren Booda
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.

what is the p/q method?

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