{"status": "success", "data": {"description_md": "The sum of the zeros, the product of the zeros, and the sum of the coefficients of the function $f(x)=ax^{2}+bx+c$ are equal. Their common value must also be which of the following? <br>\t\n\n$\\textrm{(A)}\\ \\textrm{the\\ coefficient\\ of\\ }x^{2}~~~ \\textrm{(B)}\\ \\textrm{the\\ coefficient\\ of\\ }x$\n\n$\\textrm{(C)}\\ \\textrm{the\\ y-intercept\\ of\\ the\\ graph\\ of\\ }y=f(x)$\n\n$\\textrm{(D)}\\ \\textrm{one\\ of\\ the\\ x-intercepts\\ of\\ the\\ graph\\ of\\ }y=f(x)$\n\n$\\textrm{(E)}\\ \\textrm{the\\ mean\\ of\\ the\\ x-intercepts\\ of\\ the\\ graph\\ of\\ }y=f(x)$\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 sum of the zeros, the product of the zeros, and the sum of the coefficients of the function <span class=\"katex--inline\">f(x)=ax^{2}+bx+c</span> are equal. Their common value must also be which of the following? <br/></p>&#10;<p><span class=\"katex--inline\">\\textrm{(A)}\\ \\textrm{the\\ coefficient\\ of\\ }x^{2}~~~ \\textrm{(B)}\\ \\textrm{the\\ coefficient\\ of\\ }x</span></p>&#10;<p><span class=\"katex--inline\">\\textrm{(C)}\\ \\textrm{the\\ y-intercept\\ of\\ the\\ graph\\ of\\ }y=f(x)</span></p>&#10;<p><span class=\"katex--inline\">\\textrm{(D)}\\ \\textrm{one\\ of\\ the\\ x-intercepts\\ of\\ the\\ graph\\ of\\ }y=f(x)</span></p>&#10;<p><span class=\"katex--inline\">\\textrm{(E)}\\ \\textrm{the\\ mean\\ of\\ the\\ x-intercepts\\ of\\ the\\ graph\\ of\\ }y=f(x)</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2007 AMC 12A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12A_p22", "prev": "/problem/07_amc12A_p20"}}