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2025 AMC 12B Question 8

AMC12 · 2025 AMC 12B

Question 8

There are integers $a$ and $b$ such that the polynomial $x^3 - 5x^2 + ax + b$ has $4 + \sqrt{5}$ as a root. What is $a + b?$
  1. $13$
  2. $17$
  3. $20$
  4. $30$
  5. $68$