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Q.

Total number of values of ‘a’ so that x2–x–a = 0 has integral roots, where aN and 6≤a≤100 is 

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answer is 8.

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Detailed Solution

The given equation is x2-x-a=0

Given that the roots of the above equaiton are integers, 

it implies that a must be integer, and discriminant must be perfect square

b2-4ac=1-4-a=4a+1

4a+1 must be perfect sqaure only when a=6,12,20,30,42,56,72,90

Therefore,the number of values of a is 8

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