Let $p(x)$ be a quadratic polynomial with integer coefficients which has $3+\sqrt{7}$ as a root. Compute $\frac{p(2)}{p(3)}.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $p(x)$ be a quadratic polynomial with integer coefficients which has $3+\sqrt{7}$ as a root. Compute $\frac{p(2)}{p(3)}.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{6}{7}
Let $p(x)$ be a quadratic polynomial with integer coefficients which has $3+\sqrt{7}$ as a root. Compute $\frac{p(2)}{p(3)}.$
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