Figure shows a feedback system where $$K>0$$

The range of $$k$$ for which system is stable will by given by

If the loop gain $$K$$ of a negative feedback system having a loop transfer function $$K\left( {s + 3} \right)/{\left( {s + 8} \right)^2}$$ is to be adjusted to induce a sustained oscillation then

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

For the equation, $${s^3} - 4{s^2} + s + 6 = 0$$ the number of roots in the left half of $$s$$ plane will be