Comparing degree of two polynomials via resultant

Question

I am looking for a way to compare the degree of two polynomials via resultant; I.e., given two polynomials $f(x)=f_0+f_1 x^1+\cdots+f_d x^d$ and $g(x)=g_0+g_1x^1+\cdots+g_s x^s$ in $K[f_0,\cdots,f_d,g_0,\cdots,g_s,x]$, is it possible to find a polynomial $R$ in $K[f_0,\cdots,f_d,g_0,\cdots,g_s]$ s.t. $R=0$ iff $d \leq s$? (Perhaps something like $res_x(f,g)$...)