Some inequalities for algebraic polynomials (Q1078706)

Let P(z) be a monic polynomial of degree n with P(0)\(\neq 0\). The author shows by elementary methods that there is, for each \(\theta\), a rose with n petals, passing through 0, such that both the bounded set \(B_ m(\theta)\) bounded by the rose, and \(B^ 1_ m\), the complement of the closure of \(B_ m(\theta)\) with respect to the extended plane, each contain at least one zero of P, except when all the zeros are on the boundary. He obtains further inequalities in terms of translations of the curves \(B_ m(\theta)\) and \(B^ 1_ m(\theta)\).