Given the congruence $ax^2+bx+c \equiv 0 \pmod {2^n}$, how precisely does one go about finding its roots?
I'm comfortable with quadratic congruence mod n with n odd, but 2's lack of a multiplicative inverse in $\mathbb Z/2^n \mathbb Z$ complicates matters, and the standard parity root test doesn't generally provide much help.
I suppose in $\mathbb Z/2^n \mathbb Z$ we look for roots mod 2 and apply Hensel Lifting, etc., this no different than for powers of odd primes?
What I would really appreciate is a detailed description of what one does to analyze a quadratic in a mod ring of integers with parity. To be honest I am surprised that I can't find a satisfactory exposition of this — I'm wondering if I'm thinking about it all wrong. Thanks in advance!