We fix two non-zero natural integers $n$ and $m$ as well as two polynomials $Q \in \mathbb{C}[X]$ and $R \in \mathbb{C}[X]$ of degrees $n$ and $m$ respectively. We introduce the polynomial $P = QR$ and we denote by $\lambda$ its leading coefficient and $\alpha_1, \ldots, \alpha_{n+m}$ its roots counted with multiplicity. Deduce from question 3.20 that: $$\|Q\|_{\mathbb{D}} \|R\|_{\mathbb{D}} \leq M(S)$$ where $S$ is the polynomial defined by: $$S(X) = (X-1)^{m+n} P\left(\frac{uX - v}{X - 1}\right)$$
We fix two non-zero natural integers $n$ and $m$ as well as two polynomials $Q \in \mathbb{C}[X]$ and $R \in \mathbb{C}[X]$ of degrees $n$ and $m$ respectively. We introduce the polynomial $P = QR$ and we denote by $\lambda$ its leading coefficient and $\alpha_1, \ldots, \alpha_{n+m}$ its roots counted with multiplicity.
Deduce from question 3.20 that:
$$\|Q\|_{\mathbb{D}} \|R\|_{\mathbb{D}} \leq M(S)$$
where $S$ is the polynomial defined by:
$$S(X) = (X-1)^{m+n} P\left(\frac{uX - v}{X - 1}\right)$$