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Consider the equation `x^2+2x-n=0w h e r en in Na n dn in [5,100]dot` The total number of different values of `n` so that the given equation has integral roots is `8` b. `3` c. `6` d. `4`

A

8

B

3

C

6

D

4

Text Solution

Verified by Experts

The correct Answer is:
1
`x^(2) + 2x - n = 0 rArr (x + 1)^(2) = n + 1`
`rArr x = -1 pm sqrt(n + 1)`
Thus, n + 1 should be a perfect square. Now,
`n in [5, 100] rArr n + 1 in [6, 101]`
Perfect square values of n + 1 are 9, 16, 25, 36, 49, 64, 81, 100.
Hence, number of values is 8.
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