math-ai/BlueMO
BlueMO 🚀 BlueMO: A Comprehensive Collection of Challenging Mathematical Olympiad Problems from the Little Blue Book Series BlueMO is a comprehensive and challenging dataset comprising mathematical olympiad problems paired with detailed solutions, meticulously curated from the esteemed "Little Blue Book" (小蓝书) series (Second Edition)—a vital resource for Chinese students training for national and international olympiad math competitions. Designed to… See the full description on the dataset page: https://huggingface.co/datasets/math-ai/BlueMO.
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1{2 "source_file": "./raw_volume-zh/volume8/exercise3.tex",3 "problem_type": "calculation",4 "problem": "问题3. 方程 $a x^2+b|x|+c=0(a 、 b 、 c \\in \\mathbf{R}, a \\neq 0)$ 在复数集内的根的个数是 $n$, 则 ( ).\n(A) $n$ 最大是 2\n(B) $n$ 最大是 4\n(C) $n$ 最大是 6\n(D) $n$ 最大是 8",5 "solution": "C.\n不妨设 $a=1$.\n由 $b 、 c 、|x|$ 均是实数,可知 $x^2$ 必是实数,因此 $x$ 是实数或纯虚数.\n若 $x$ 是实数 $u$, 则 $u^2+b u+c=0(u \\geqslant 0)$ 或 $u^2-b u+c=0(u<0)$.\n若 $x$ 是纯虚数 $v \\mathrm{i}$, 则 $v^2-b v-c=0(v \\geqslant 0)$ 或 $v^2+b v-c=0(v<0)$.\n对 $b 、 c$ 异号时, 有 6 个根满足要求; 对其他的情况, 满足要求的根都不足 6 个.",6 "remark": "",7 "figures": []8}