If , , and | matrix 3&f(1)&f(2) (1)&f(2)&f(3) (2)&f(3)&f(4) matrix |=k(- )^2(- )^2( -…

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

If α,β≠0\alpha,\beta\ne0, f(n)=αn+βnf(n)=\alpha^n+\beta^n, and ∣3f(1)f(2)f(1)f(2)f(3)f(2)f(3)f(4)∣=k(−α)2(−β)2(α−β)2,\left|\begin{matrix}3&f(1)&f(2)\\f(1)&f(2)&f(3)\\f(2)&f(3)&f(4)\end{matrix}\right|=k(-\alpha)^2(-\beta)^2(\alpha-\beta)^2, then kk is equal to: (1) 11 (2) −1-1 (3) αβ\alpha\beta (4) 1αβ\frac{1}{\alpha\beta}

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