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Question

Consider the equation x2+2xn=0, where n [5,100]. Total number of different values of 'n' so that the given equation has integral roots is


A

4

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B

6

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C

8

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D

3

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Solution

The correct option is C

8


The roots of the equation are
2¯¯¯¯+44x(n)2
2¯¯¯¯+4(1+n)2
2¯¯¯¯+21+n2
1¯¯¯¯+1+n

It will be an integer when 1+n is a perfect square. Given n [5,100]. 1+n will be a perfect square when n=8, 15,24,35,.......99
Number of different values = 8


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