Let $p(y)$, $q(y)$ be irreducible polynomials in $y$, of the same degree $d$ (over some field $K$). Assume also that the resultant of $p$ and $q$ is $1$ or $-1$ (not sure if it is necessary here).
I'm interested in finding the leading term (in regard to $x$) of the polynomial disc$[q(y)x-p(y)]$ (the discriminant is in regard to $y$). I tried working on the definition but I'm not sure how to salvage $x$ from the product. Some products of the inverse images of $x$ under $p\div q$ seem to be calculatable but I'm unsure how to connect the parts.