Mathematical background

Let $P$ the polynomial:

$$P=a_0+a_1x+\ldots+a_nx^n$$

and let $\vert P\vert$ be:

$$\vert P\vert={\rm Max}_{i =0}^{i =n} \vert a_i\vert$$

The minimal distance $\Delta$ between the real roots of $P$ is such that [26]:

$$\Delta > \sqrt{\frac{8}{n^{n+2}}}\frac{1}{1+\vert P\vert^n}$$