A method is considered for constructing on a computer areas in the parameter space of linear automatic control systems (ACS), within which the value of the direct quality indicator do not exceed the required one. To solve the problem, it is necessary to repeatedly construct and analysis the transient process in the ACS, as well as construction and analysis the D-partition hodograph. The construction of these characteristics for complex systems can turn into a significant problem associated with the choice of the step of change and the maximum frequency value, the integration step and the maximum integration time value. In turn, to solve the problem, the researched characteristics are needed not as a whole, but only their individual points, with the help of which the boundaries of the desired areas are determined. It is proposed to determine the presence of these points by positive real roots of specially constructed algebraic equations, that doesn't require enumeration of the values of frequency and time characteristics, thus does not require their direct construction. The proposed solution to the problem can significantly reduce the time of preliminary assessment of the quality of the researched ACS.