Let $k$ be a field $f,g\in k[x,y]$ be two polynomials. The resultant $R\in k[x]$ is a polynomial function of the coefficients of $f$ and $g$, such that $f$ and $g$ gave a common zero (in an extension) if and only if $R(a)=0$. Further it is know that there are polynomials $A$ and $B$ of degrees in $y$, one less that those of $g$ and $f$ respectively such that $Af+Bg=R$.
My question is $$k[x,y]/(f,g) \cong k[x]/(R) ?$$