Let $p(x)=x^n+a_{n-1}x^{n-1}+....+a_0$ be a polynomial with real coefficients and leading coefficient of $1$. Let $M_1=1+max (|a_0|,|a_1|,|a_2|,...,a_{n-1}|)$ and Let $M_2=max (1,|a_0|+|a_1|+|a_2|...+|a_{n-1}|)$. Finally let $M=(M_1,M_2)$.
Then prove that every zero of $p(x)$ lies between $-M$ and $M$.
I approached this problem by induction but it was just a mess. So how do I proceed??