Question 67
We are given a natural number $d$. Find all open intervals of maximum length $I \subseteq \mathbb{R}$ such that for all real numbers $a_0, a_1, \dots, a_{2d-1}$ inside the interval $I$, the polynomial $P(x) = x^{2d} + a_{2d-1}x^{2d-1} + \dots + a_1x + a_0$ has no real roots.