# Find the value of the polynomial

Algebra Level 5

Let $$Q(x) = a_0 + a_1x + a_2x^2 + \cdots + a_nx^n$$ be a polynomial with integer coefficients, and $$0 \le a_i < 3$$ for all $$0 \le i \le n$$.

Given that $$Q\big(\sqrt 3\big) = 20 + 17\sqrt 3$$, what is the value of $$Q(2)$$?

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