The following paper http://www.math.leidenuniv.nl/~evertse/05-discres.pdf looks at the binary form $\sum \alpha_ix^iy^{m-i} where i ranges from 0 to m. It then defines the discriminant.

It's well known that for binary quadratic forms how to find a lower bound using the discriminant. I was wondering if analogous theorems hold for a form of arbitrary degree.

Ultimately I would like to find a lower bound in terms of the variable y for this binary form I'm working on.

A little more details:

I'm trying to show that the binary form $x^{n-1}+x^{n-2}y\alpha^2+x^{n-3}y^2\alpha^3+...+y^{n-1}\alpha^{n-1}$ is bounded below by $c*y^{n-1}$ or something similar where c is some explicit constant.