How can I tell Mathematica to keep solutions of this equation up to second order in q?
Solve[Det[{{I x + a, b, 0}, {I f - I q^2 O,
I x + d - q^2 c, -I q^2 e}, {0, h, I x + g}}] == 0, x]
sol = x /.Solve[Det[{{I x + a, b, 0}, {I f - I q^2 O,
I x + d - q^2 c, -I q^2 e}, {0, h, I x + g}}] == 0, x]
Normal[Series[sol, {q, 0, 2}]]