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2021 AMC 12A Question 22

AMC12 · 2021 AMC 12A

Question 22

Suppose that the roots of the polynomial $P(x) = x^3 + ax^2 + bx + c$ are $\cos\tfrac{2\pi}{7},$ $\cos\tfrac{4\pi}{7},$ and $\cos\tfrac{6\pi}{7},$ where angles are in radians. What is $abc?$
  1. $-\dfrac{3}{49}$
  2. $-\dfrac{1}{28}$
  3. $\dfrac{\sqrt[3]{7}}{64}$
  4. $\dfrac{1}{32}$
  5. $\dfrac{1}{28}$