# Visualize a root of one variable equation with Manipulate?

Posted 7 months ago
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 Hello. I am trying to visualize root of third degree one variable equation. Delta^3-C0*delta+2==0, C is between [0,10]. But there occurs an error. Could you help to fix this problem. Thanks a lot. Here is the code: Manipulate[ f1 = \[CapitalDelta]0^3 - ะก*\[CapitalDelta]0 + 2; sol1 = FindRoot[f1 == 0, {\[CapitalDelta]0, 0.9}]; Plot[ f1, {\[CapitalDelta]0, 0, 1}, PlotRange -> 0.1, Epilog -> {{PointSize[0.03], Point[{\[CapitalDelta]0 /. sol1, 0}]}, Text["\!$$\*SubscriptBox[\(\[CapitalDelta]$$, $$0$$]\)=", {0.75, \ -0.05}], Text[ ToString[N[\[CapitalDelta]0 /. sol1, 10]], {0.9, -0.05}]}] , {C0, 0.1, 5}] 
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Posted 7 months ago
 Manipulate[g = d^3 - C0*d + 2; sol = NSolve[g == 0 && -4 < d < 4, d, Reals]; Column[{StringForm["C0= and Roots=.", C0, d /. sol], Plot[g, {d, -4, 4}, ImageSize -> 300, Epilog -> {PointSize[0.02], Point[Transpose[{d /. sol, g /. sol}]]}, PlotRange -> {-15, 15}]}], {{C0, 3.5}, 0, 10}] Or: f[x_, c_] := x^3 - c*x + 2 Manipulate[roots = x /. NSolve[f[x, C0] == 0, x]; pts = Select[{#, 0} & /@ roots, Element[#[[1]], Reals] &] // Union; {xmin, xmax} = If[Length[pts] > 1, MinMax[pts[[All, 1]]], {-2, 2}]; Column[{StringForm["C0= and Roots=.", C0, d /. sol], Plot[f[x, C0], {x, xmin, xmax}, Epilog -> If[Length[pts] > 0, {Red, AbsolutePointSize[6], Point[pts]}, {}], ImageSize -> 500]}], Grid[{{Control[{{C0, 0}, 0, 10, 0.1, Appearance -> "Labeled"}]}}]] Regards MI.