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Q.

Consider the equation x² + 2x–n = 0, $n \in N and n \in [5, 100]$ , the number of different values of ‘n’ so that the given equation has integral roots, is

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answer is 8.

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Detailed Solution

$\begin{array}{l} x = \frac{- 2 \pm \sqrt{4 + 4 η}}{2} = - 1 \pm \sqrt{1 + η} \\ n + 1 is a perfect square \\ η = 8, 15, 24, 35, 48, 63, 80, 99 . . . . (8) \end{array}$

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