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!Fancy cubic

Author: anonymous
Problem has been solved: 58 times

Русский язык | English Language



The cubic polynomial $ P (x) $ is given. For a certain number $ a $, we define $P_1(x) = x^2 + (a-29) x-a $ and $ P_2(x) = 2x^2 + (2a-43)x + a$. It turned out that $ P(x) $ is divisible by $ P_1(x) $ and $ P_2(x) $. Find the largest possible value of $ a $.





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