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Note: This is similar to, but easier than, a previous question I asked here. It is a different question! I'm hoping this one might get an answer because it concerns a standard algorithm, whereas the ...

If $q$ is a prime what is the best method to compute roots of a quadratic polynomial $f(x)\equiv0\bmod q^2$ which is of form $x^2+bx+c\equiv0\bmod q^2$ where $b^2-4c\equiv0\bmod q$ and $gcd(b,q)=1$ ...