Question

If $\left| \begin{matrix} x + \alpha & \beta & \gamma \\ \alpha & x + \beta & \gamma \\ \alpha & \beta & x + \gamma \end{matrix} \right|$ = 0, then x is equal to

• A. 0, α² + β² + γ²
• B. 1, α + β + γ
• C. 0, – (α + β +γ )
• D. 0, (α + β + γ)

Answer 1

Answer: (C)

0, – (α + β +γ )

Answer 2

If we put x = 0 then Three rows are same so

(x – 0)² is factor of ∆

Now, C₁ → C₁ + C₂ + C₃ &

Take common (x + α + β + γ)

So ∆ = x² (x + α +β + γ) ⇒ x = 0, –α – β – γ