All these given roots are contained in option C.
The given equation is :
[tex]9x^{3}+9x^{2}-4x-4=0[/tex]
[tex]9x^{2}(x+1)-4(x+1)=0[/tex]
[tex](9x^{2}-4)(x+1)=0[/tex]
[tex]9x^{2}-4=0,x+1=0[/tex]
[tex]x^{2}=\frac{4}{9},x=-1[/tex]
[tex]x=\frac{2}{3},x=-1[/tex]
Roots = [tex]-1,\frac{-2}{3} ,\frac{2}{3}[/tex]
Hence these lie in between [tex](\frac{-3}{2} ,\frac{3}{2})[/tex]
