Suppose $f(z)=z^n+a_1z^{n-1}+...+a_n$ for which $a_1,a_2,...,a_n\in \mathbb C$. Prove that the following polynomial has only one positive real root like $\alpha$ \[x^n+\Re(a_1)x^{n-1}-|a_2|x^{n-2}-...-|a_n|\] and the following polynomial has only one positive real root like $\beta$ \[x^n-\Re(a_1)x^{n-1}-|a_2|x^{n-2}-...-|a_n|.\] And roots of the polynomial $f(z)$ satisfy $-\beta \le \Re(z) \le \alpha$.