A rational game 2

Algebra Level 3

A polynomial with integer coefficients P(x)=anxn+an1xn1++a0P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}, with ana_{n} and a0a_{0} being coprime positive integers, has one of the roots 23\frac{2}{3}. Find the second smallest possible value of a0+ana_{0}+a_{n}.


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