MathNet 2009-part-02 — 175 problems (EN–VI) Question 165

Prove that the equation $x^n - a_1 x^{n-1} - a_2 x^{n-2} - \dots - a_{n-1} x - a_n = 0$, where $a_k \ge 0$, $1 \le k \le n$, does not have two distinct positive solutions.