{"status": "success", "data": {"description_md": "For a certain complex number $c$, the polynomial\n\n$$P(x) = (x^2 - 2x + 2)(x^2 - cx + 4)(x^2 - 4x + 8)$$has exactly 4 distinct roots. What is $|c|$?\n\n$\\textbf{(A) } 2 \\qquad \\textbf{(B) } \\sqrt{6} \\qquad \\textbf{(C) } 2\\sqrt{2} \\qquad \\textbf{(D) } 3 \\qquad \\textbf{(E) } \\sqrt{10}$\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>For a certain complex number  <span class=\"katex--inline\">c</span> , the polynomial</p>&#10;<p> <span class=\"katex--display\">P(x) = (x^2 - 2x + 2)(x^2 - cx + 4)(x^2 - 4x + 8)</span> has exactly 4 distinct roots. What is  <span class=\"katex--inline\">|c|</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 2 \\qquad \\textbf{(B) } \\sqrt{6} \\qquad \\textbf{(C) } 2\\sqrt{2} \\qquad \\textbf{(D) } 3 \\qquad \\textbf{(E) } \\sqrt{10}</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": 3, "problem_name": "2019 AMC 12A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12A_p15", "prev": "/problem/19_amc12A_p13"}}