Let $p(x)$ be quadratic with rational coefficients.  If $p(\sqrt{7}) = 22$ and $p(\sqrt{11}) = 30,$ then find $p(\sqrt{17}).$
Question:
Let $p(x)$ be quadratic with rational coefficients.  If $p(\sqrt{7}) = 22$ and $p(\sqrt{11}) = 30,$ then find $p(\sqrt{17}).$
Answer:
Let's think step by step.

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Let $p(x)$ be quadratic with rational coefficients.  If $p(\sqrt{7}) = 22$ and $p(\sqrt{11}) = 30,$ then find $p(\sqrt{17}).$
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