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I have to analyze the complex regions of variable c which is define obtained with InverseLaplace help in the form

Re[c] + Im[c] == -10 s^2 - (1/(2 Pi)
NIntegrate[1/Q[k, s], {k, -∞, ∞}])^-1;

Q[k_, s_] := 5 k^4 - 3 (-k 2 + s)^2;

I applied the RootLocusPlot on this polynomial, but I am not sure what I got. Is this complex plane of c variable? I need to see what will happen with c when s goes to $∞$ or $0$, but in my figure I can not understand that? Is there another command to plot diagram depends on complex solutions?

RootLocusPlot[
  TransferFunctionModel[Unevaluated[{{-10 s^2 - 5 k^4 - 3 (-k 2 + s)^2}}], 
                        s, SamplingPeriod ->None, SystemsModelLabels -> None], 
  {k, 0, 0.8}]

enter image description here

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  • $\begingroup$ Since you didn't get answers here you are now asking a new question? $\endgroup$ – Öskå Mar 12 '14 at 10:57
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    $\begingroup$ @Öskå I picked up the point just on the part of the question already asked. To take a look is it better for understanding because the problem is more complex that I thought.My previous question is large and consists of few parts. I didn't get any sign for further analysis. $\endgroup$ – Pipe Mar 12 '14 at 11:06
  • $\begingroup$ You could have simply edit your last question since you are trying to answer it through this new question :) $\endgroup$ – Öskå Mar 12 '14 at 17:14
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If you have a polynomial $poly[s, k]$ in the complex variable $s$ and parameter $k$ and would like to see the loci of the roots of $poly[s, k]==0$ as $k$ varies, use the syntax RootLocusPlot[1/poly[s,k],{k,kmin,kmax},FeedbackType->None].

Assuming I understood your question correctly, in your example the result looks like this.

RootLocusPlot[1/(-10 s^2 - 5 k^4 - 3 (-k 2 + s)^2), {k, 0, 0.8}, FeedbackType -> None]

enter image description here

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