JEE-Mains 2014 (5/30)

Algebra Level 4

\[\displaystyle \left| \begin{array}{} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) & 1+f(4) \end{array} \right|= k(1-\alpha)^2(1-\beta)^2(\alpha-\beta)^2\]
If \(\alpha,\beta \neq 0\), and \(f(n)=\alpha^n+\beta^n\), then \(k\) is equal to :

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