Solving equation approximately

Questions
,
1

Look at this equation. Clearly this is not solvable. but a=c=0 reduces the equation which gives two solutions. now I want to find an approximate solution of the original equation which gives the same solution of the reduced equation after substituting a=c=0 in the solution. Is there any way to do that?
Thanks in advance.

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polynomial.nb (6.76 KB)

2

I am not sure what you have in mind, but here is an attempt:

Manipulate[{NSolve[2  a  Q^4 + 5  r^4  (-4  Q^2 -
        2  r  (-3  M + r) + 
        3  c  r^(1 - 3 \[Omega])  (1 + \[Omega])) == 0,
   r, Reals],
  Style[{{r -> 1/2  (3  M - Sqrt[9 M^2 - 8 Q^2])},
    {r -> 1/2  (3  M + Sqrt[9 M^2 - 8 Q^2])}},
   Red]},
 {{a, 0}, -1, 1},
 {{c, 0}, -1, 1},
 {{M, 1}, 0, 2},
 {{Q, 1}, 0, 1},
 {\[Omega], 0, 1}]
3

Thanks for the reply. I need analytical expression for r in terms of other variables. [omega] lies between -1 and -1/3. Other parameters may take any positive value. Even an approximate expression would do good.

4

You may try AsymptoticSolve:

AsymptoticSolve[
 2   a   Q^4 + 5   r^4   (-4   Q^2 - 2   r   (-3   M + r) +
      3   c   r^(1 - 3  \[Omega])   (1 + \[Omega])) == 0,
 {r, 1/2   (3   M + Sqrt[9  M^2 - 8  Q^2])},
 {{a, c}, {0, 0}, 1}]
5

This asymptoticsolve worked very well. Thank you very much.