Question

Consider the equation x^2 + 2x - n = 0, where nÎN and 5 £ n £ 100. total number of different values of 'n' so that

the given equation has integral roots is​

Answer 1

Given x2−2x−n=0

The given equation has integral roots. 

The sum of the roots =2

Let the roots be 1−k,k+1 , where k is a positive integer. 

Product of the roots =1−k^2=−n

⇒k^2−1=n

n∈[5,100]

5≤n≤100

6≤n+1≤101

6≤k^2≤101

⇒k2=9,16,25,36,64,49,64,81,100

For k=3,4,5,6,7,8,9,10

Hence, there will be 8 corresponding values of n.

Answer 2

Step-by-step explanation:

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