About interrelation of roots and factors of characteristic polynomials of differentiating filters

The conformity between area of polynomials roots and area of meanings of his coefficients on an example of polynomial of the second order is investigated. For polynomials on whose roots the certain restrictions are imposed, the area of possible meanings of coefficients is defined. The way of a choice of coefficients of characteristic polynomial of the differentiating filter of automatic control system is offered, providing satisfactory distribution of his roots and, hence, quality of processes in a contour of fast movements.