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How to find the values of $a$ in

(-2 Sqrt[6] a^2 b^2 M - 2 Sqrt[6] a^2 Sqrt[1 - b^2] M) r - 
 2 Sqrt[6] M r^3 + r^2 (4 Sqrt[6] M^2 + 2 a^2 b^2 Sqrt[ϵ]) + 
 r^4 Sqrt[ϵ] + a^4 Sqrt[ϵ] Cos[θ]^4=0

where there is no real solutions to $r$.

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    $\begingroup$ I think it would help if you clarify which variables are real, imaginary, or complex. @Jose E Calderon 's answer gives a general solution without making assumptions about the domains of the variables, but with more information it could easily be modified to do so. $\endgroup$ – nadlr Nov 22 '16 at 19:09
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Solve[(-2 Sqrt[6] a^2 b^2 M - 2 Sqrt[6] a^2 Sqrt[1 - b^2] M) r - 
   2 Sqrt[6] M r^3 + 
   r^2 (4 Sqrt[6] M^2 + 2 a^2 b^2 Sqrt[\[Epsilon]]) + 
   r^4 Sqrt[\[Epsilon]] + a^4 Sqrt[\[Epsilon]] Cos[\[Theta]]^4 == 0,
  a]
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  • $\begingroup$ I don't think this answers my question. Because I want the values $a$ for the solutions of $r$ in the equation are real, i.e. the roots are not real. $\endgroup$ – gbd Nov 19 '16 at 7:10

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