The open loop transfer function of a unity gain negative feedback system is given by,

G(s)=K/s²+4s-5

The range of K for which the system is stable, is

To find the range of $K$ for which the system is stable, we need to analyze the characteristic equation of the closed-loop system.

Given the open-loop transfer function of a unity gain negative feedback system:
$G\left(s\right)=\frac{K}{s^2+4s-5}$

For a unity feedback system, the feedback path gain is:
$H\left(s\right)=1$

The characteristic equation of a closed-loop system is given by:
$1+G\left(s\right)H\left(s\right)=0$

Substituting the given values into the characteristic equation:
$1+\frac{K}{s^2+4s-5}$

Multiplying the entire equation by the denominator