On the location of zeros of generalized derivative

Let P(z) = Pi(n)(v=1) (z - z(v)), be a monic polynomial of degree n, then, G gamma inverted right perpendicularP(z)inverted left perpendicular = Sigma(n)(k=1) gamma k Pi(n)(v=1,v not equal k) (z - z(v)), where gamma = (gamma(1), gamma(2), ..., gamma(n)) is a n-tuple of positive real numbers with Sigma(n)(k=1) gamma k = n, be its generalized derivative. The classical Gauss-Lucas Theorem on the location of critical points have been extended to the class of generalized derivative[4]. In this paper, we extend the Specht Theorem and the results proved by A.Aziz [1] on the location of critical points to the class of generalized derivative.