Dec 15, 2015
I feel like one time you mentioned how the average of the roots of a quadratic became the root of its derivative? Came across something today that reminded me of this... If you check out the Gauss–Lucas thm wiki page they mention it and a slight generalization to degree 3 (Marden's theorem) which turns out to be pretty crazy.
WP: Gauss-Lucas Theorem
The theorem states that the roots of P' all lie within the convex hull of the roots of P, that is the smallest convex polygon containing the roots of P.
huh! i always suspected...
the proof is pretty neat too, actually :V
