Root loci of system of [5;0] class

Root hodographs of systems described by the equation $(a_0p^5+a_1p^4+a_2p^3+a_3p^2+a_4p+a_5)+K=0$ in the complex - frequency plane p are considered. Relations are found between the coefficients $a_i$ determining the types of root trajectory. From the analysis of types of root hodographs, the possible dynamic properties of such systems are established, allowing their investigation and calculation to be more expediently conducted.