JEE Advanced Model Paper 14 with solutions for online practice

Let the expression is of the form (x - α) (x - β) (x - γ) (x - δ)
It can be a perfect square if either both expressions are simultaneously perfect squares or both roots common, i.e. (k−2)2 + 8k = 0 and k2 - 4 (2k - 4) = 0 or

2−k

k

=

−2k

2k−4

Solving we get k can take only one value