Visualize a root of one variable equation with Manipulate?

Questions
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1

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 - ?*\[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}]
2

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.

3

Thanks a lot, it works. In addition, is it possible to make show the numerical value of C?

4

I updated my answer. You can also press a small plus(Show Animation Control) to see values C0.