About this blog

I feel this blog as a reflection of my thoughts to myself , and sometimes as a public diary, and the last she is my best friend to share my thoughts who says never a "oh no! ,you shouldn't....That Disgusts...."

Solving a quartic(biquadratic) equation and some ideas for solving bigger than quintics as galois ruled out the radical way for quintics and bigger

The types of quartic solvers, I learned in my Intermediate education are,
1. Ferraris Method (square-completion of the even powered part of the
    polynomial and then using a consistency condition to get a new cubic in an
    unknown)
2. Descartes Method (product of conjugate quadratics)
3. Lagrange's Method (using resolvent cubic)
4. I doubt there is one more method.

For Cubics,
 1. cardon's method:(original work by Scipione del Ferro (1465-1526), passed by Tartaglia to cardon).
2. Vieta's Geometric approach by seperating equations for real part and imaginary.


For quintics and above, I thought of using the singular perturbation technique to add extra terms that make the a polynomial to shrink to lower orders.
   Over internet , I found some analysis for linear equations using singular quadratics .

I see some scope in this area , as Galois ruled out the Radical ways for Quintics , but still we can think of Non-Radical ways ,like this one. and one more important idea is to use transcendentals which don't comply with these finite polynomials.

Note:
Kulkarni, R. G. (2006): “Unified method for solving general polynomial equations of degree less than five”  , is a worth reading.