Clearly, your function is non-finite at x=0. There is a factor of x^2 in its denominator.
Regardless, fzero() is the wrong tool for analyzing a rational function. Just use roots() to get the roots of the numerator polynomial.
r=[roots([1 0 4 -10]).' ,-4/3];
r=real( r( abs(imag(r))<1e-10 ))
And, of course, you must make sure that none of the numerator roots coincide with any denominator roots, but that is obvious here by inspection.