{"status": "success", "data": {"description_md": "The quadratic equation $x^2 + mx + n = 0$ has roots that are twice those of $x^2 + px + m = 0$, and none of $m$, $n$, and $p$ is zero. What is the value of $n/p$?\n\n$\\mathrm{(A)} 1 \\qquad \\mathrm{(B)} 2 \\qquad \\mathrm{(C)} 4 \\qquad \\mathrm{(D)} 8 \\qquad \\mathrm{(E)} 16$", "description_html": "<p>The quadratic equation  <span class=\"katex--inline\">x^2 + mx + n = 0</span>  has roots that are twice those of  <span class=\"katex--inline\">x^2 + px + m = 0</span> , and none of  <span class=\"katex--inline\">m</span> ,  <span class=\"katex--inline\">n</span> , and  <span class=\"katex--inline\">p</span>  is zero. What is the value of  <span class=\"katex--inline\">n/p</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)} 1 \\qquad \\mathrm{(B)} 2 \\qquad \\mathrm{(C)} 4 \\qquad \\mathrm{(D)} 8 \\qquad \\mathrm{(E)} 16</span> </p>\n<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": "2005 AMC 10B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10B_p17", "prev": "/problem/05_amc10B_p15"}}