Assumption $d>2$ on Proposition 2.12 from Knapp's Elliptic Curves

Question

I'm going through Knapp's book on elliptic curves and I got stuck in a minor detail.

This is a part of the proof of Proposition 2.12:

I could understand everything except for this little detail: Where are we making use of the assumption $d>2$?

I will post some pictures about the references that the proof makes use of, in order for you to understand the whole argument.

Proposition 2.7 and identity (2.12):

Lemma 2.11:

Answer 1

If $d = 1$ then the Hessian is the zero matrix at every point, so Lemma 2.11 does not apply. And the case $d = 2$ is discussed immediately after the end of your first image. In this case $F$ itself defines a conic and the author concludes that every nonsingular point of $F = 0$ is a flex.