{"status": "success", "data": {"description_md": "Let $ P(z) = z^3 + az^2 + bz + c$, where $ a$, $ b$, and $ c$ are real. There exists a complex number $ w$ such that the three roots of $ P(z)$ are $ w + 3i$, $ w + 9i$, and $ 2w - 4$, where $ i^2 = - 1$. Find $ |a + b + c|$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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 $ P(z) = z^3 + az^2 + bz + c$, where $ a$, $ b$, and $ c$ are real. There exists a complex number $ w$ such that the three roots of $ P(z)$ are $ w + 3i$, $ w + 9i$, and $ 2w - 4$, where $ i^2 = - 1$. Find $ |a + b + c|$.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 4, "problem_name": "2010 AIME II Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/10_aime_II_p08", "prev": "/problem/10_aime_II_p06"}}