Question 101
Given a polynomial $p(x) = a_{2n+1}x^{2n+1} + a_{2n}x^{2n} + \dots + a_1x + a_0$ of odd degree with positive coefficients $a_0, a_1, \dots, a_{2n}, a_{2n+1}$.
Prove that there exists a permutation (may be, trivial) of coefficients of $p(x)$ such that the polynomial obtained has exactly one real root.
(A. Voidelevich)
Prove that there exists a permutation (may be, trivial) of coefficients of $p(x)$ such that the polynomial obtained has exactly one real root.
(A. Voidelevich)