$$s^4+12s^3+22s^2+(20+K)s+2K=0$$
I don't understand, how can I sketch the root locus? Can anybody help me to understand?
2026-05-05 21:28:02.1778016482
Skecth the root locus with respect to K for the characteristic equation.
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The equation you present has "roots" with respect to $s$, that is, values of $s$ that cause the equation to be satisfied (values that make the left-hand side zero). However, as you change the gain $K$, those roots move around in the complex $s$-plane. The "locus" of all the points in the complex plane where the roots move around as $K$ changes are called the root locus.
There are rules for sketching these things by hand. Usually though you have numerator and denominator, or an open loop transfer function. Are you sure you have presented us with all of the information you are given?