{"status": "success", "data": {"description_md": "Let $f(x)= \\sqrt{ax^2+bx}$.  For how many real values of $a$ is there at least one positive value of $b$ for which the domain of $f$ and the range of $f$ are the same set?\n\n$\\mathrm{(A) \\ 0 } \\qquad \\mathrm{(B) \\ 1 } \\qquad \\mathrm{(C) \\ 2 } \\qquad \\mathrm{(D) \\ 3 } \\qquad \\mathrm{(E) \\ \\mathrm{infinitely \\ many} }$\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>Let  <span class=\"katex--inline\">f(x)= \\sqrt{ax^2+bx}</span> .  For how many real values of  <span class=\"katex--inline\">a</span>  is there at least one positive value of  <span class=\"katex--inline\">b</span>  for which the domain of  <span class=\"katex--inline\">f</span>  and the range of  <span class=\"katex--inline\">f</span>  are the same set?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A) \\ 0 } \\qquad \\mathrm{(B) \\ 1 } \\qquad \\mathrm{(C) \\ 2 } \\qquad \\mathrm{(D) \\ 3 } \\qquad \\mathrm{(E) \\ \\mathrm{infinitely \\ many} }</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": "2003 AMC 12A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/03_amc12A_p24"}}