1. Tardigrade
  2. Question
  3. Mathematics
  4. If α, β, γ are the roots of x3+b x+c=0, then the determinant Δ=|α β γ β γ α γ α β| equals

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Q. If $\alpha, \beta, \gamma$ are the roots of $x^3+b x+c=0$, then the determinant $\Delta=\begin{vmatrix}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta\end{vmatrix}$ equals

Determinants

Solution:

In this case $\alpha+\beta+\gamma=0$.
Thus, from (1) in solution to question 26 , we get $\Delta=0$.