{"status": "success", "data": {"description_md": "The [[quadratic equation]] $x^2+mx+n$ has roots twice those of $x^2+px+m$, and none of $m,n,$ and $p$ is zero. What is the value of $n/p$?\n\n$\\mathrm{(A)}\\ {{{1}}} \\qquad \\mathrm{(B)}\\ {{{2}}} \\qquad \\mathrm{(C)}\\ {{{4}}} \\qquad \\mathrm{(D)}\\ {{{8}}} \\qquad \\mathrm{(E)}\\ {{{16}}}$\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 [[quadratic equation]]  <span class=\"katex--inline\">x^2+mx+n</span>  has roots twice those of  <span class=\"katex--inline\">x^2+px+m</span> , and none of  <span class=\"katex--inline\">m,n,</span>  and  <span class=\"katex--inline\">p</span>  is zero. What is the value of  <span class=\"katex--inline\">n/p</span> ?</p>&#10;<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>&#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": 3, "problem_name": "2005 AMC 12B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc12B_p13", "prev": "/problem/05_amc12B_p11"}}