If alpha "and" beta are the roots of the...

If `alpha "and" beta` are the roots of the equations
`x^(2)-2x+4=0`,find the value of `|{:(sumalpha,sumalpha^(2),sumalpha^(3)),(sumalpha^(2),sumalpha^(3),sumalpha^(4)),(sumalpha^(3),sumalpha^(4),sumalpha^(5)):}|`.

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