# Plotting solutions of a 4th order polynomial equation

I have a polynomial equation of the fourth order, which has 44 roots depending on a variable parameter s1. For each s1 I have 44 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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mathematica.stackexchange.com/q/15637/5478
– Kuba
Mar 31 ’14 at 22:27

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

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1

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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]}]

Thank you Suba Thomas. This is it.
– Pipe
Apr 1 ’14 at 16:20