A critically damped, continuous-time, second order system, when sampled, will have ( in Z domain)

Consider a characteristic equation given by
s⁴ + 3s³ + 5s² + 6s + K + 10 = 0.
The condition for stability is

Consider a closed-loop system shown in fig. (a) below. The root locus for it is shown in fig. (b). The closed-loop transfer function for the system is

Minimum number of 2-input NAND gates required to implement the function, f=($$\overline X $$+$$\overline Y $$)(Z+W) is