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Daniel J Smith Custom TMUA alpha · Q14

Algebra

Let aa be a real number for which the equation

∣x−1∣+∣x+1∣=a|x-1|+|x+1|=a

has finitely many distinct real solutions for xx. Let kk be this nonnegative integer number of solutions.

Which one of the following is the complete list of all possible values of kk?

A00 only
B0,10,1
C0,20,2
D1,21,2
E0,1,20,1,2
F22 only

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