If $α, β$ and $γ$ are the roots of the equation $x^3+px+q=0$ (with $p≠0$ and $q≠0$), the value of the determinant $\begin{vmatrix}α& β&γ\\β&γ&α\\γ&α&β\end{vmatrix}$, is

none of these

It is given that $α, β, γ$ are the roots of the given equation.

$∴α+β+γ=0$

So,

$Δ=\begin{vmatrix}α& β&γ\\β&γ&α\\γ&α&β\end{vmatrix}$

$Δ=\begin{vmatrix}α+β+γ& β&γ\\α+β+γ&γ&α\\α+β+γ&α&β\end{vmatrix}$  [Using $C_1→C_1+ C_2 + C_3$]

$Δ=\begin{vmatrix}0& β&γ\\0&γ&α\\0&α&β\end{vmatrix}=0$   $[∵α+β+γ=0]$