Consider the equation x2+2x−n=0, where n ∈ [5,100]. Total number of different values of 'n' so that the given equation has integral roots is
8
The roots of the equation are
−2¯¯¯¯+√4−4x(−n)2
−2¯¯¯¯+√4−(1+n)2
−2¯¯¯¯+2√1+n2
−1¯¯¯¯+√1+n
It will be an integer when √1+n is a perfect square. Given n ∈ [5,100]. √1+n will be a perfect square when n=8, 15,24,35,.......99
⇒Number of different values = 8