The General Conic in Trilinears

The discrimination of the conics given by the general equation.

Let uα²+vβ²+wγ²+2u^'βγ+2v^'γα+2w^'αβ=0

be the conic, which will be denoted by

(u,v,w,u^',v^',w^')(α,β,γ)²=0.