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Quartic Equations


I have 3 quartic equations which are
a1*x^4 + b1*x^3 + c1*x^2 + d1*x +e1 = 0   -- (1) a2*x^4 + b2*x^3 +
c2*x^2 + d2*x +e2 = 0   --(2) a3*x^4 + b3*x^3 + c3*x^2 + d3*x +e3 = 0  
and another 4th equation.
a1, b1, ...,a2, ... are in terms of other 3 unknowns, A, B and C.

Thus I have 4 equations and 4 unknowns, x, A, B and C.
Normally, we would solve the equations simultaneously.  However, as
these are ridiculously huge equations, it really pushes Mathematica to
the limit when it is used in order to solve it because it takes days.
Thus, another way of takling that problem, which I can think of, is
equate the coefficients  b1/a1=b2/a2=....., and c1/a1=c2/a2=... and
di/a1=... when the 3 quartics produce the exact same four roots.  
However, my problem here is the 3 quartics dont give the exact same four
roots.  Instead they only give two same roots out of four.  Therfore,
is there any other way of getting those unknowns?
I am really stuck at the moment.  Apparently, I killed the whole univ
network last week due to using Mathematica to solve the problem. I am
not sure if Mathematica can do that.


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