{"status": "success", "data": {"description_md": "For how many ordered pairs $(a,b)$ of integers does the polynomial $x^3+ax^2+bx+6$ have $3$ distinct integer roots?\n\n$\\textbf{(A)}\\ 5 \\qquad\\textbf{(B)}\\ 6 \\qquad\\textbf{(C)}\\ 8 \\qquad\\textbf{(D)}\\ 7 \\qquad\\textbf{(E)}\\ 4$\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>For how many ordered pairs  <span class=\"katex--inline\">(a,b)</span>  of integers does the polynomial  <span class=\"katex--inline\">x^3+ax^2+bx+6</span>  have  <span class=\"katex--inline\">3</span>  distinct integer roots?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 5 \\qquad\\textbf{(B)}\\ 6 \\qquad\\textbf{(C)}\\ 8 \\qquad\\textbf{(D)}\\ 7 \\qquad\\textbf{(E)}\\ 4</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": "2023 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc12B_p15", "prev": "/problem/23_amc12B_p13"}}