The integer 'n' for which n 2 + 19n + 92 is a perfect squar…

Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

The integer 'n' for which n 2 + 19n + 92 is a perfect square-

–8

–11

11 Let f be a real valued function satisfying

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CHECK THE SOLUTION.

(a, c)

n 2 + 19n + 92 = x 2

⇒ 4(n 2 + 19n + 92) = 4x 2

⇒ (2n + 19) 2 + 7 = 4x 2

⇒ 4x 2 – 7 must be square of integer

Let 4x 2 – 7 = k 2

So 4x 2 – k 2 = 7 ⇒ (2x – k)(2x + k) = 7

from above ⇒ x = 2

(2n + 19) 2 + 7 = 16

⇒ (2n + 19) 2 = 9

⇒ n = –8 or –11

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