{"status": "success", "data": {"description_md": "How many quadratic polynomials with real coefficients are there such that the set of roots equals the set of coefficients? (For clarification: If the polynomial is $ax^2+bx+c,a\\neq 0,$ and the roots are $r$ and $s,$ then the requirement is that $\\{a,b,c\\}=\\{r,s\\}$.)\n\n$\\textbf{(A) } 3 \\qquad\\textbf{(B) } 4 \\qquad\\textbf{(C) } 5 \\qquad\\textbf{(D) } 6 \\qquad\\textbf{(E) } \\text{infinitely many}$\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>How many quadratic polynomials with real coefficients are there such that the set of roots equals the set of coefficients? (For clarification: If the polynomial is  <span class=\"katex--inline\">ax^2+bx+c,a\\neq 0,</span>  and the roots are  <span class=\"katex--inline\">r</span>  and  <span class=\"katex--inline\">s,</span>  then the requirement is that  <span class=\"katex--inline\">\\{a,b,c\\}=\\{r,s\\}</span> .)</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 3 \\qquad\\textbf{(B) } 4 \\qquad\\textbf{(C) } 5 \\qquad\\textbf{(D) } 6 \\qquad\\textbf{(E) } \\text{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": "2019 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12B_p22", "prev": "/problem/19_amc12B_p20"}}