For what values of K does the polynomial s4+8s3+24s2+32s+K=0 have roots with zero real parts?

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State Variable Analysis and Design topics include: Concepts of state, state variables and state model, solutions of state equations, controllability and observability, pole placement by state feedback, observer systems and state models for linear continuous-time systems. State-variable analysis, also known as state-space analysis, is a procedure that can be used to analyze and design systems. It can be applied to linear and nonlinear circuits, as well as circuits with time-varying parameters.  A state variable is a characteristic of a system that can be described by a set of first-order... Show more

For what values of K does the polynomial s<sup>4</sup>+8s<sup>3</sup>+24s<sup>2</sup>+32s+K=0 have roots with zero real parts?