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Let alpha "and " beta be the roots of th...

Let `alpha "and " beta` be the roots of the equation `ax^(2)+bx+c=0. Let S_(n)=alpha^(n)+beta^(n) "for" n ge`1. Evaluate the determinant `|{:(3,1+S_(1),1+S_(2)),(1+S_(1),1+S_(2),1+S_(3)),(1+S_(2),1+S_(3),1+S_(4)):}|`

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