Consider the equation x 2 + 2 x - n = 0 , where n ∈ N and n ∈ 5 ,   100 . The number of different values of n so that the given equation has integral roots, is

Step-by-step solution

x 2 + 2 x - n = 0 ;   n ∈ 5 ,   100 D will be a perfect square, D = 4 + 4 n = 4 1 + n ⇒ 1 + n is a perfect square ⇒ 1 + n = 9 ,   16 ,   25 ,   36 ,   49 ,   64 ,   81 ,   100 ⇒ n = 8 ,   15 ,   24 ,   35 ,   48 ,   63 ,   80 ,   99 Therefore, 8 values are possible.