Mathematics

Problem

\alpha

and

\beta

are the roots of the equations

x^2 - 2x + 4 = 0, \text{ find the value of } \begin{vmatrix} \Sigma \alpha & \Sigma \alpha^2 & \Sigma \alpha^3 \\ \Sigma \alpha^2 & \Sigma \alpha^3 & \Sigma \alpha^4 \\ \Sigma \alpha^3 & \Sigma \alpha^4 & \Sigma \alpha^5 \end{vmatrix}