Really interesting one

If a,b,c ε R are distinct then the condition on a,b,c for which the equation
1x-a+1x-b+1x-c+ 1x-b-c-a=0
has real roots is

(a)a+b+c≠0,a≠0

(b)a-b-c≠0,a≠0

(c)2a=b+c
(d) none of these

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