An elementary, but very useful tool for proving inequalities for polynomials with restricted zeros is the Bernstein or Lorentz representation of polynomials. In
Let p(z)=a_0+a_1z+a_2z~2+a_3z~3+···+a_nz~n be a polynomial of degree n.Rivlin[12]proved that if p(z)≠0 in the unit disk,then for 0<r≤1,max|z|=r