Suppose f(z)=zn+a1zn−1+...+an for which a1,a2,...,an∈C. Prove that the following polynomial has only one positive real root like αxn+ℜ(a1)xn−1−∣a2∣xn−2−...−∣an∣and the following polynomial has only one positive real root like βxn−ℜ(a1)xn−1−∣a2∣xn−2−...−∣an∣.
And roots of the polynomial f(z) satisfy −β≤ℜ(z)≤α.