Consider the following Nyquist plots of loop transfer functions over $$\omega = 0$$ to $$\omega = \infty .$$ Which of these plots represents a stable closed loop system?

The Bode magnitude plot of $$H\left( {j\omega } \right) = {{{{10}^4}\left( {1 + j\,\omega } \right)} \over {\left( {10 + j\,\omega } \right){{\left( {100 + j\omega } \right)}^2}}}$$ is

A closed loop system has the characteristic function $$\left( {{s^2} - 4} \right)\left( {s + 1} \right) + K\left( {s - 1} \right) = 0.$$
Its root locus plot against $$K$$ is

The algebraic equation
$$F\left( s \right) = {s^5} - 3{s^4} + 5{s^3} - 7{s^2} + 4s + 20$$
$$F\left( s \right) = 0$$ has