{"status": "success", "data": {"description_md": "For certain real numbers $a$, $b$, and $c$, the polynomial $$g(x) = x^3 + ax^2 + x + 10$$has three distinct roots, and each root of $g(x)$ is also a root of the polynomial $$f(x) = x^4 + x^3 + bx^2 + 100x + c.$$What is $f(1)$?\n\n$\\textbf{(A)}\\ -9009 \\qquad\\textbf{(B)}\\ -8008 \\qquad\\textbf{(C)}\\ -7007 \\qquad\\textbf{(D)}\\ -6006 \\qquad\\textbf{(E)}\\ -5005$\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 certain real numbers  <span class=\"katex--inline\">a</span> ,  <span class=\"katex--inline\">b</span> , and  <span class=\"katex--inline\">c</span> , the polynomial  <span class=\"katex--display\">g(x) = x^3 + ax^2 + x + 10</span> has three distinct roots, and each root of  <span class=\"katex--inline\">g(x)</span>  is also a root of the polynomial  <span class=\"katex--display\">f(x) = x^4 + x^3 + bx^2 + 100x + c.</span> What is  <span class=\"katex--inline\">f(1)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ -9009 \\qquad\\textbf{(B)}\\ -8008 \\qquad\\textbf{(C)}\\ -7007 \\qquad\\textbf{(D)}\\ -6006 \\qquad\\textbf{(E)}\\ -5005</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": "2017 AMC 12A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12A_p24", "prev": "/problem/17_amc12A_p22"}}