Solution 5

It is given that x [ n ] is real, and that X ( z ) has exactly two poles with one of the pole at . Since, x [ n ] is real, the two poles must be complex conjugates of each other. Thus, the other pole of the system is at . Also, it is given that X ( z ) has two zeros at the origin. Therefore, X ( z ) will have the following form:

for some constant K to be determined. Finally, it is given that . Substituting this in the previous equation, we get K = 2. Thus,

Since x [ n ] is right sided its ROC is (note that both poles have magnitude ).