Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Consider the equation x 2 + 2x - 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
Text Solution
Verified by ExpertsThe correct answer is:
8
(8)
Sol. x 2 + 2x - n = 0; n 
[5, 100]
D will be a perfect square,
D = 4 + 4n = 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.
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