Exercise

Let $p \in \mathbb {Z}[X]$ and of fifth degree with only the terms for $x^5$, $x^4$ and $x^3$ known, the terms for $x^2$, $x$ and $1$ are not known.

$$p=x^5 - 5x^4 - 35x^3 + \cdots$$ The ( five ) roots of $p$ form an arithmetic sequence. Find the roots of $p$.