Until the end of part A, we assume that all roots of $p$ are stable and have multiplicity 1.
Let $h$ be the polynomial of degree $n$ defined by $h(X) = X p'$, where $p'$ is the derivative polynomial of $p$. We denote by $h_0$ and $(p')_0$ the reciprocal polynomials of $h$ and $p'$ respectively.
Show that $h = np - \lambda (p')_0$, then that $h_0 = \lambda(np - Xp')$.