  In this paper, we provide a simple proof of a generalization of the
Gauss-Lucas theorem. By using methods of D-companion matrix, we get the
majorization relationship between the zeros of convex combinations of
incomplete polynomials and an origin polynomial. Moreover, we prove that the
set of all zeros of all convex combinations of incomplete polynomials coincides
with the closed convex hull of zeros of the original polynomial. The location
of zeros of convex combinations of incomplete polynomials is determined.
