Let P(X)=a2n+1X2n+1+a2nX2n+...+a1X+a0 be a polynomial with all positive coefficients. Prove that there exists a permutation (b2n+1,b2n,...,b1,b0) of numbers (a2n+1,a2n,...,a1,a0) such that the polynomial Q(X)=b2n+1X2n+1+b2nX2n+...+b1X+b0 has exactly one real root.