I am facing the following problem : I have an equation which could write
$$ F(x_1(Y))-F(x_2(Y)) = 0 $$
$x_1$ and $x_2$ are the largest and smallest roots of a cubic equation; their definition involves a function $Y$ I do not know and for which I try to have a Taylor expansion at $Y=0$.
The problem is that, at $Y=0$, $x_1=x_2$ and I am stuck; no way to get anything.
Any idea and suggestion will be welcomed.
Thank you very much.