Let's have a multi-variable high degree polynomial $f(x_1, x_2, \dots, x_n)$. I am looking for efficient way to figure out if there are any roots in real numbers for:
$0 \le x_1 \le 1\\ 0 \le x_2 \le 1\\ \dots\\ 0 \le x_n \le 1$
Can you give some hints, theorems or algorithms for performing such tasks. And I don't need to find roots exactly. I just need to know if there are roots or not.