1)

The value of x obtained from the equation

|x+αβγγx+βααβx+γ|=0

will be


A) 0 and -(α+β+γ)

B) 0 and α+β+γ

C) 1 and αβγ

D) 0 and α2+β2+γ2

Answer:

Option A

Explanation:

Given |x+αβγγx+βααβx+γ|=0

Operate C→ 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

|1βγ0xαγ00x|=0

x2 = 0 → x = 0

.'. Solutions of the equation x = 0, -(α+β+γ)