Using Rouché prove that $a_0\geq a_1 \geq ... \geq a_n > 0$ the polynomial $P(z)=a_n z^n + ... + a_1 z + a_0$ has no roots $|z|<1$
$0 < a_0 \leq a_1 \leq \cdots \leq a_n$, show $ p_n(z) = a_0 z^n + a_1 z^{n-1} + \cdots + a_{n-1} z + a_n = 0$ has no root in $|z| < 1$