If both the roots of the equation $$x^2 – 2kx + k^2 – 4 = 0$$    lie between $$– 3$$ and $$5,$$ then which one of the following is correct ?

Solution :
$$\eqalign{ & {x^2} - 2kx + {k^2} - 4 = 0 \cr & \Rightarrow {\left( {x - k} \right)^2} - {2^2} = 0 \cr & \Rightarrow \left( {x - k - 2} \right)\left( {x - k + 2} \right) = 0 \cr & \Rightarrow x = k + 2,k - 2. \cr & \Rightarrow k + 2 < 5\,\& \,k - 2 > - 3 \cr & \Rightarrow k < 3\,\& \,k > - 1 \cr & \Rightarrow - 1 < k < 3 \cr} $$