Question

Consider the equation x^2+2x-n=0, where n belongs to n and n £[5,100]. total number of different values of n so that the given equation has integral roots is

Answer 1

Answer: 8

Explanation:

Root will be an integer when the “square root of (1+n)” must be a perfect square.

Between the numbers 5 to 100, perfect squares are 9,16,25,36,49,64,81,100

So, the values of n are 8,15,24,35,48,63,80,99 (so that n+1 is a perfect square)

Therefore, there are 8 different values of n between 5 and 100 so that the roots are integers.