Question

If a, b, g are the roots of the equation x³ + px + q = 0 then the value of $\left| \begin{matrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \end{matrix} \right|$ is –

• A. q
• B. 0
• C. p
• D. p² – 2q

Answer 1

Answer: (B)

0

Answer 2

Since a, b, g are the roots

\ a + b + g = $\frac{- b}{a}$ = 0

So $\left| \begin{matrix} \alpha + \beta + \gamma & \beta & \gamma \\ \alpha + \beta + \gamma & \gamma & \alpha \\ \alpha + \beta + \gamma & \alpha & \beta \end{matrix} \right|$ = $\left| \begin{matrix} 0 & \beta & \gamma \\ 0 & \gamma & \alpha \\ 0 & \alpha & \beta \end{matrix} \right|$= 0