Let

and

be two non-constant polynomials in two variables with complex coefficients.
We study the relation between the degrees of the resultant of

and

with respect to

and

and the topological degree

of the application

The special case

was considered by Sakkalis
[#!a3!#]. As an application, we give a constructive proof of the known fact, that an injective morphism

is actually an automorphism of

.