In an IS-LM framework extended with price adjustment dynamic equations, the LM curve adjusts instantaneously while aggregate demand adjusts sluggishly. The system exhibits saddle-path dynamics if:

This is the Blanchard-Kahn condition. For a system with predetermined (state) variables and jump variables to have a unique saddle-path solution, the number of stable roots (negative real parts) must equal the number of predetermined variables, and the number of unstable roots (positive real parts) must equal the number of jump variables. Option (B): if all roots are positive, the system is unstable in every direction and no convergent path exists. Option (C): in a two-variable system a saddle has one positive and one negative root. The determinant is the product of the roots, so it is negative, not positive. Option (D): a saddle requires at least one forward-looking jump variable. Option (E): complex roots with positive real parts give an unstable spiral, not a saddle. Hence the correct option is (A).