{"status": "success", "data": {"description_md": "Let $p(x) = x^3 + ax^2 + bx + c$, where $a$, $b$, and $c$ are complex numbers.  Suppose that\n\n$$p(2009 + 9002\\pi i) = p(2009) = p(9002) = 0$$What is the number of nonreal zeros of $x^{12} + ax^8 + bx^4 + c$?\n\n$\\textbf{(A)}\\ 4\\qquad \\textbf{(B)}\\ 6\\qquad \\textbf{(C)}\\ 8\\qquad \\textbf{(D)}\\ 10\\qquad \\textbf{(E)}\\ 12$\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>Let <span class=\"katex--inline\">p(x) = x^3 + ax^2 + bx + c</span>, where <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span> are complex numbers.  Suppose that</p>&#10;<p><span class=\"katex--display\">p(2009 + 9002\\pi i) = p(2009) = p(9002) = 0</span>What is the number of nonreal zeros of <span class=\"katex--inline\">x^{12} + ax^8 + bx^4 + c</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 4\\qquad \\textbf{(B)}\\ 6\\qquad \\textbf{(C)}\\ 8\\qquad \\textbf{(D)}\\ 10\\qquad \\textbf{(E)}\\ 12</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2009 AMC 12A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12A_p22", "prev": "/problem/09_amc12A_p20"}}