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Contradiction between Routh's algorithm and checking with some value

I am designing a control system controlled by some microcontroller K:

![](https://electrical.codidact.com/uploads/qauslimvnjz3clqkdw46elnqoe3i)

The open loop gain is $G_{o}(s) = \frac{K}{s(s^{2}+4s+3)}$

and the closed loop gain is obviously $G_{c}(s) = \frac{K}{s(s^{2}+4s+3)+K}$

I tried finding the critical frequency but found something else interesting while trying to find the critical frequency.

I applied Ruth's algorithm to the denominator of the closed loop gain and I get this result:

![Image_alt_text](https://electrical.codidact.com/uploads/sl6l8lgwpu0xaszte0fe7cyoukpq)

Obviously for a stable system k doesnt exist but this seemed super odd so I decided to set k = 2 and find all the roots [using a calculator](https://www.symbolab.com/solver/roots-calculator/roots%20x%5E%7B3%7D%2B4x%5E%7B2%7D%2B3x%2B2?or=input) and I found that the root is in the left half plane of the Re,Im plane so the system SHOULD be stable. So what am I doing wrong?