Mathematical background

Let $P(x)$ be an univariate polynomial of degree $n$:

$$P(x)= x^n + a_{1} x^{n-1}+.....a_n=0$$

Assume that $P$ has $n$ real roots. Then [23] all roots are contained in the interval whose end-point are given by the two solutions of the quadratic equation:

$$nx^2+2a_1x+[2(n-1)a_2-(n-2)a_1^2]=0$$