Question

Total number of integral values of ‘n’ so that the equation x² + 2x –n = 0 (n ∈ N) and n ∈ [5, 100] has integral roots is

(a) 2 

(b)  4

(c)  6

(d) 8 and ∈[5,100] 

Answer 1

Correct option (d) 8 and ∈[5,100] 

Explanation:

x² + 2x – n = 0

⇒ x² + 2x + 1 = n + 1

⇒ (x + 1)² = n + 1

 x + 1 = ± √n + 1

⇒ n + 1 should be perfect square

n∈[5,100]

n + 1 ∈[6,101]

Perfect squares in the given interval are

9, 16, 25, 36, 49, 64, 81, 100

8 values