Effect of zero coefficient in polynomial in Routh Hurwitz?
What happens if we have zero in place of any coefficient in our polynomial? Will that indicate that the system is unstable?


The first check on seeing the characteristic equation of a system is -- if any of the coefficients in the polynomial is non-positive.


If any of the coefficients is 0 or -ve, then the system is not stable.
If all coefficients are positive, then the system may or may not be stable. 



  Let say we have zero instead of '2' in the above polynomial, will this make the system unstable?


Yea, that's right.