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Albania IMO TST 2012 equation

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May 18, 2013
algebra proposedalgebra

Problem Statement

It is given the equation x4−2ax3+a(a+1)x2−2ax+a2=0x^4-2ax^3+a(a+1)x^2-2ax+a^2=0. a) Find the greatest value of aa, such that this equation has at least one real root. b) Find all the values of aa, such that the equation has at least one real root.
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