# $P(x)$ with coefficient $\pm1$

Find all polynomial $P(x)$ with coefficient $\pm1$ and have all real roots.

My attempted work :

Let $P(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$

$-P(x) = -a_nx^n - a_{n-1}x^{n-1} - ... - a_1x - a_0$

$P(x)$ have all real roots $\Leftrightarrow -P(x)$ have all real roots.

WLOG, $a_n = 1$

$P(x) = x^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$

Let $r_1, r_2, ..., r_n$ be roots of the equation.

$P(x) = (x-r_1)(x-r_2)...(x-r_n)$