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I have a polynomial equation of the fourth order, which has $4$ roots depending on a variable parameter s1. For each s1 I have $4$ solutions. I need a LinePlot of all roots to see how they move in the complex plane when the parameter s1 changes. I can solve my equation but I don't know how to plot all the roots together on one diagram (points connected with line for each solution).

poly = -6.110000000000001`*^6 k^4 + 1000.` s1^2 + 60.335263000000005`(-5.` k + s1)^2;

Table[ NSolve[ poly == 0, k], {s1, {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9}}]
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You have already asked quite similar question and I think you've seen e.g. this Factoring a two variable polynomial in a special way, in fact, this answers your question. – Artes Mar 31 '14 at 22:31
I don't understand light and dark green and lines there while roots moving – Pipe Mar 31 '14 at 23:14
up vote 6 down vote accepted

You can use RootLocusPlot.

poly = -6.110000000000001`*^6 k^4 + 1000.` s1^2 + 60.335263000000005` (-5.` k + s1)^2;

RootLocusPlot[1/poly, {s1, 0, 1}, FeedbackType -> None, 
PoleZeroMarkers -> {"ParameterValues" -> Range[0.1, 0.9, 0.1]}]

enter image description here

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Thank you Suba Thomas. This is it. – Pipe Apr 1 '14 at 16:20
Glad it solved your problem. – Suba Thomas Apr 1 '14 at 16:37

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