If α, β ≠ 0, and f( n )=α^n +β^n and |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)| = K (1-α)^2 (1-β)^2(α-β)^2, then K is equal…

If $\displaystyle \alpha, \beta \neq 0$, and $\displaystyle f(\mathrm{n})=\alpha^{\mathrm{n}}+\beta^{\mathrm{n}}$ and $$\begin{aligned} & \left|\begin{array}{ccc} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) & 1+f(4) \end{array}\right| \\ & =\mathrm{K}(1-\alpha)^2 \quad(1-\beta)^2(\alpha-\beta)^2, \text { then } \mathrm{K} \text { is } \end{aligned} $$ equal to :