Plotting the sign of a two-variables function

Question

I have a continous function f(x,y), and I want the 2D plot of its sign. I then created a function

sign=Sign[f]

and used ContourPlot: what I obtained is this graph

where the blue region corresponds to -1 and the yellow region to 1. Can I get rid of the white region? It does not depend on the function, as there are points in it with -1 or 1 sign.

Thank you in advance!

EDIT: the exact expression of f, in its original variables h and mu, is

1/mu^4*( 0.0562706 (-0.308221 + Sqrt[0.1 + h + mu]) (-2.01155 + 
   1. Sqrt[0.1 + h + mu]) (-0.324443 - 3.24443 h - 11.7611 mu + 
   1. Sqrt[0.1 + h + mu]) (-0.049713 - 0.49713 h - 1.8021 mu + 
   1. Sqrt[0.1 + h + mu]) (-0.0431301 - 0.431301 h + 1. mu - 
   0.737425 Sqrt[0.1 + h + 1.09109 mu]) (-0.0431301 - 0.431301 h + 
   1. mu + 0.133495 Sqrt[0.1 + h + 1.09109 mu]) (-0.309516 + Sqrt[
   0.1 + h + 1.09109 mu]) (1.70977 + 1. Sqrt[0.1 + h + 1.09109 mu]))

Answer 1

Add the options PlotRange -> All and Exclusions -> None:

ContourPlot[Sign[f[h, mu]], {h, 0, 100}, {mu, 0, 20}, 
 Contours -> {{0}}, ContourStyle -> Red, PlotPoints -> 100, 
 PlotRange -> All, Exclusions -> None]

Answer 2

With your data, I get a complete different plot. For clarity., I only plot the zero contour:

f[h_, mu_] := 
  1/mu^4*(0.0562706 (-0.308221 + Sqrt[0.1 + h + mu]) (-2.01155 + 
        1. Sqrt[0.1 + h + mu]) (-0.324443 - 3.24443 h - 11.7611 mu + 
        1. Sqrt[0.1 + h + mu]) (-0.049713 - 0.49713 h - 1.8021 mu + 
        1. Sqrt[0.1 + h + mu]) (-0.0431301 - 0.431301 h + 1. mu - 
        0.737425 Sqrt[0.1 + h + 1.09109 mu]) (-0.0431301 - 
        0.431301 h + 1. mu + 
        0.133495 Sqrt[0.1 + h + 1.09109 mu]) (-0.309516 + 
        Sqrt[0.1 + h + 1.09109 mu]) (1.70977 + 
        1. Sqrt[0.1 + h + 1.09109 mu])) // Simplify;

ContourPlot[f[h, mu] == 0, {h, 0, 100}, {mu, 0, 20}, 
 FrameLabel -> {"h", "mu"}, ContourLabels -> Automatic]

Answer 3

Or RegionPlot

RegionPlot[{f[h, mu] < 0, f[h, mu] > 0}, {h, 0, 100}, {mu, 0, 20}, 
 FrameLabel -> {"h", "mu"}, PlotPoints -> 200, 
 PlotStyle -> {Red, Green}, BoundaryStyle -> Yellow]