# Routh's stability criterion: zeros of the auxiliary polynomial and of its derivative

When using RH criterion and using the auxiliary equation special case, which of the following is true?

1. The auxiliary equation $$A(s)=0$$ gives some(or all) of the symmetrical poles.

2. The differentiated auxiliary equation $$\displaystyle \frac{\mathrm{d}A(s)}{\mathrm{d}s}=0$$ gives some(or all) of the symmetrical poles.

I have seen both of them mentioned either separately or together in different books. I am really confused on which one is actually correct.

After solving a few problems I have observed that $$1$$ generally holds, it might be a coincidence. If someone could explain if I am missing something or if either of them(aforementioned cases) is wrong, it would be really helpful.