{"status": "success", "data": {"description_md": "Monic quadratic polynomials $P(x)$ and $Q(x)$ have the property that $P(Q(x))$ has zeros at $x=-23, -21, -17,$ and $-15$, and $Q(P(x))$ has zeros at $x=-59,-57,-51$ and $-49$. What is the sum of the minimum values of $P(x)$ and $Q(x)$? \n\n$\\textbf{(A)}\\ -100 \\qquad \\textbf{(B)}\\ -82 \\qquad \\textbf{(C)}\\ -73 \\qquad \\textbf{(D)}\\ -64 \\qquad \\textbf{(E)}\\ 0$\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>Monic quadratic polynomials  <span class=\"katex--inline\">P(x)</span>  and  <span class=\"katex--inline\">Q(x)</span>  have the property that  <span class=\"katex--inline\">P(Q(x))</span>  has zeros at  <span class=\"katex--inline\">x=-23, -21, -17,</span>  and  <span class=\"katex--inline\">-15</span> , and  <span class=\"katex--inline\">Q(P(x))</span>  has zeros at  <span class=\"katex--inline\">x=-59,-57,-51</span>  and  <span class=\"katex--inline\">-49</span> . What is the sum of the minimum values of  <span class=\"katex--inline\">P(x)</span>  and  <span class=\"katex--inline\">Q(x)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ -100 \\qquad \\textbf{(B)}\\ -82 \\qquad \\textbf{(C)}\\ -73 \\qquad \\textbf{(D)}\\ -64 \\qquad \\textbf{(E)}\\ 0</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": "2010 AMC 12B Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12B_p24", "prev": "/problem/10_amc12B_p22"}}