Answer:
Option A
Explanation:
Given |x+αβγγx+βααβx+γ|=0
Operate C1 → C1 + C2 + C3
|x+α+β+γβγx+α+β+γx+βαx+α+β+γβx+γ|=0
(x+α+β+γ)|1βγ1x+βα1βx+γ|=0
x = -(α+β+γ)
Again if
|1βγ1x+βα1βγ|=0→
|1βγ0xα−γ00x|=0
x2 = 0 → x = 0
.'. Solutions of the equation x = 0, -(α+β+γ)