{"status": "success", "data": {"description_md": "There is a smallest positive real number $a$ such that there exists a positive real number $b$ such that all the roots of the polynomial $x^3-ax^2+bx-a$ are real. In fact, for this value of $a$ the value of $b$ is unique. What is the value of $b?$\n\n$\\textbf{(A)}\\ 8\\qquad\\textbf{(B)}\\ 9\\qquad\\textbf{(C)}\\ 10\\qquad\\textbf{(D)}\\ 11\\qquad\\textbf{(E)}\\ 12$\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>There is a smallest positive real number  <span class=\"katex--inline\">a</span>  such that there exists a positive real number  <span class=\"katex--inline\">b</span>  such that all the roots of the polynomial  <span class=\"katex--inline\">x^3-ax^2+bx-a</span>  are real. In fact, for this value of  <span class=\"katex--inline\">a</span>  the value of  <span class=\"katex--inline\">b</span>  is unique. What is the value of  <span class=\"katex--inline\">b?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 8\\qquad\\textbf{(B)}\\ 9\\qquad\\textbf{(C)}\\ 10\\qquad\\textbf{(D)}\\ 11\\qquad\\textbf{(E)}\\ 12</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": "2016 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12A_p25", "prev": "/problem/16_amc12A_p23"}}