Suppose that we have proven the following theorem :
Let P be a non constant complex polynomial. Then the convex hull of the roots of P' are included in the convex hull of the roots of P :
$ Conv(P') \subset Conv(P) $
Then how could we deduce the following ?
$ \forall v \in \mathbb{C} \: \: \: Conv(P') \subset Conv(P-v) $