TH-TMO 2011 Problem 7

Let $a,b,c,d \in \mathbb{R}^+$ and suppose that all roots of the equation \begin{align*} x^5-ax^4+bx^3-cx^2+dx=1 \end{align*} are real. Prove \begin{align*} \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} \le \frac{3}{5} \end{align*}