{"status": "success", "data": {"description_md": "The polynomial $f(x) = x^{4} + ax^{3} + bx^{2} + cx + d$ has real coefficients, and $f(2i) = f(2 + i) = 0.$ What is $a + b + c + d?$<br>\t\n\n$\\mathrm{(A)}\\ 0 \\qquad \\mathrm{(B)}\\ 1 \\qquad \\mathrm{(C)}\\ 4 \\qquad \\mathrm{(D)}\\ 9 \\qquad \\mathrm{(E)}\\ 16$\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>The polynomial <span class=\"katex--inline\">f(x) = x^{4} + ax^{3} + bx^{2} + cx + d</span> has real coefficients, and <span class=\"katex--inline\">f(2i) = f(2 + i) = 0.</span> What is <span class=\"katex--inline\">a + b + c + d?</span><br/></p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 0 \\qquad \\mathrm{(B)}\\ 1 \\qquad \\mathrm{(C)}\\ 4 \\qquad \\mathrm{(D)}\\ 9 \\qquad \\mathrm{(E)}\\ 16</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": 3, "problem_name": "2007 AMC 12A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12A_p19", "prev": "/problem/07_amc12A_p17"}}