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12. The equation X-2x-n=0 where ne N and ne15.20). The total number ofdifferent values of n for which equation has integral roots is

Answer»

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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.

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