Question

How many roots of the following polynomial are in the right half-plane, in the left half-plane, on the jw-axis? (4 points) P(s) = s5 - 2s+100s- 200 (note the missing s terms)

Answer 1

Given polynomial Fenction P(s) = 55- 284 +1008 - 200. criteria. By using Routh- Heeswitz the can be tabulated given polynomial as follows. sol o 100 841 -2 -200 Auxillary Equation O(E) - 200 265) = -254-200 Differentiate A E -16000 a = -883 -200 Roots of the The total number of = 5. given pargnomial pcs) Here two sign changes occur beloco XCS)= -259–200. he Auxillary Equation from a8 to € and e to -1600 which is negative.

considey Auxill0014 Equation X08)= -259- 200. roots of the Auxillary Equation Total number of = 4 on present the left side of the plane Number of Roots = 2 below Auxillary Equation left right side of the roots present on the Nmber of = 2 Equatico Auxillery plane belao su axis Roots present on the Neember of Now consider given polynomical pcs) = 55_259 + 1005 – 200 Roots = 5 Total number of Roots present on the left side of the Namber of plane = 3. right side of the of Roots Number present on the plane = 2. ice axes Number of Roots present on the