lf both roots of the equation $x^{2} - 2 a x + a^{2} - 1 = 0$ lie in the interval $(- 3, 4)$ , then sum of the possible integral values of $a$ is

0

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2

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4

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1

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Solution

The correct option is C $2$
Given that,
$x^{2} - 2 a x + a^{2} - 1 = 0$
$\Rightarrow (x - a - 1) (x - a + 1) = 0$
$\Rightarrow x = a + 1 o r x = a - 1$
As per the given interval,
$a - 1 > - 3$ and $a + 1 < 4$
$\Rightarrow a > - 2$ and $a < 3$
$\Rightarrow a = - 1, 0, 1, 2$
$\Rightarrow S u m = 1 + 0 - 1 + 2 = 2$

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