Question

The roots of the equation $\left| \begin{matrix} x & \alpha & 1 \\ \beta & x & 1 \\ \beta & \gamma & 1 \end{matrix} \right|$= 0 are independent of -

• A. α
• B. β
• C. γ
• D. All of these

Answer 1

Answer: (A)

α

Answer 2

$\left| \begin{matrix} x - \beta & \alpha - x & 0 \\ 0 & x - \gamma & 0 \\ \beta & \gamma & 1 \end{matrix} \right|$=0

⇒ (x–β) (x–γ) = 0

Hence roots are independent of α