Types of root trajectory of linear and linearized fourthorder systems

The root hodographs of fourth-order systems described by the characteristic equation $(a_0p^4+a_1p^3+a_2p^2+a_3p+a_4) +К=0$ are considered. In the plane of the two parameters M and N, which are functions of $a_i$, regions determining all the possible types of root trajectory are isolated. From the analysis of types of hodographs, the general dynamic properties of such systems are established, allowing their investigation and calculation to be simplified.