[math] \newcommand{\mathds}{\mathbb}[/math]

Establish with full details the resultant formula

[[math]] R(P,Q)= \begin{vmatrix} p_k&&&q_l\\ \vdots&\ddots&&\vdots&\ddots\\ p_0&&p_k&q_0&&q_l\\ &\ddots&\vdots&&\ddots&\vdots\\ &&p_0&&&q_0 \end{vmatrix} [[/math]]

and discuss as well what happens in the context of the discriminant.