# A rational game

Algebra Level 3

A polynomial with integer coefficients $P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}$, with $a_{n}$ and $a_{0}$ being coprime positive integers, has one of the roots $\dfrac{2}{3}$. Find the smallest possible value of $a_{0}+a_{n}$. For complete set, click here

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