I am trying to solve the following quartic equation eq = -w^4 + w^3 x Sqrt[1 - ϵ^2] + (w^3 X Sqrt[1 - ϵ^2])/ϵ + w^2 x X ϵ - (w^2 x X)/ϵ + w^2 y^2 ϵ - (w^2 y^2)/ϵ - w^2 ϵ - w^2/ϵ + (w x Sqrt[1 - ϵ^2])/ϵ + w X Sqrt[1 - ϵ^2] - 1 == 0; I know that for $y=0$ this equation can be factorised as (w^2 - w x Sqrt[1 - ϵ^2] + ϵ) (w^2 ϵ - w X Sqrt[1 - ϵ^2] + 1) == 0 so that for $x=X=y=0$, the four solutions are $$|w_{1,2}|^2 = \epsilon , \quad |w_{3,4}|^2 = 1/ \epsilon.$$ However, when I f...
