Show that $p_0$, the reciprocal polynomial of $p$, satisfies $$\forall x \in \mathbf{R}^* \quad p_0(x) = x^n p(1/x)$$ and deduce that $$p_0 = a_n \prod_{j=1}^{n} \left(1 - \alpha_j X\right)$$
Show that $p_0$, the reciprocal polynomial of $p$, satisfies
$$\forall x \in \mathbf{R}^* \quad p_0(x) = x^n p(1/x)$$
and deduce that
$$p_0 = a_n \prod_{j=1}^{n} \left(1 - \alpha_j X\right)$$