{"status": "success", "data": {"description_md": "Suppose that the roots of the polynomial $P(x)=x^3+ax^2+bx+c$ are $\\cos \\frac{2\\pi}7,\\cos \\frac{4\\pi}7,$ and $\\cos \\frac{6\\pi}7$, where angles are in radians. What is $abc$?\n\n$\\textbf{(A) }{-}\\frac{3}{49} \\qquad \\textbf{(B) }{-}\\frac{1}{28} \\qquad \\textbf{(C) }\\frac{\\sqrt[3]7}{64} \\qquad \\textbf{(D) }\\frac{1}{32}\\qquad \\textbf{(E) }\\frac{1}{28}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Suppose that the roots of the polynomial  <span class=\"katex--inline\">P(x)=x^3+ax^2+bx+c</span>  are  <span class=\"katex--inline\">\\cos \\frac{2\\pi}7,\\cos \\frac{4\\pi}7,</span>  and  <span class=\"katex--inline\">\\cos \\frac{6\\pi}7</span> , where angles are in radians. What is  <span class=\"katex--inline\">abc</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }{-}\\frac{3}{49} \\qquad \\textbf{(B) }{-}\\frac{1}{28} \\qquad \\textbf{(C) }\\frac{\\sqrt[3]7}{64} \\qquad \\textbf{(D) }\\frac{1}{32}\\qquad \\textbf{(E) }\\frac{1}{28}</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2021 AMC 12A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12A_p23", "prev": "/problem/21_amc12A_p21"}}