Fixed points of a quadratic equation over parameter ‘a’: dx/dt = (x^2) - a

Manipulate[
Show[{
Plot[x^2-a,{x,-1,1},PlotRange->{-1,2},Frame->True,FrameLabel->{"x","dx/dt"}],
Graphics[{PointSize[Large],Point[Transpose[{Re[x/.Solve[x^2-a==0]],{0,0}}]]}]
}],{a,-1,1}]

Fixed points of a cubic equation across parameters ‘a’, ‘b’: dx/dt = -(x^3)+ax+b

Manipulate[
Show[{
Plot[-x^3+a*x+b,{x,-3,3},PlotRange->{-3,3},Frame->True,FrameLabel->{"x","dx/dt"}],
Graphics[{PointSize[Large],Point[Transpose[{Re[x/.Solve[-x^3+a*x+b==0]],{0,0,0}}]]}]
}],
{a,-1,10},{{b,0},-1,1}]