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All the values of m for which both the roots of the equation $x^{2} - 2 mx + m^{2} - 1 = 0$ are greater than –2 but less than 4, lie in the interval

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$- 2 < m < 0$

$m > 3$

$- 1 < m < 3$

$1 < m < 4$

answer is C.

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Detailed Solution

$(x - m)^{2} - 1 = 0 \Rightarrow x = m - 1, m + 1 are roots$

$given condition⇒, m - 1 > - 2 and m + 1 < 4$

$\Rightarrow m > - 1 and m < 3 ∴ - 1 < m < 3$

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