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, a² + b²+ g²
• B. 1, a + b+ g
• C. 0, – (a + b+ g)
• D. 0, (a + b+ g)

Answer 1

Answer: (C)

0, – (a + b+ g)

Answer 2

By putting x = 0

all the three columns are identical so x² is a factor

C₁ ® C₁ + C₂ + C₃ then (x + a + b + g) is also a factor