The values of ‘a’ for which $(a^{2} - 1) x^{2} + 2 (a - 1) x + 2$ is positive for any x are

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Solution

The correct option is D
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We know that the expression $a x^{2}$ + bx + c > 0 for all x, if a > 0 and $b^{2}$ < 4ac

$∴ (a^{2} - 1) x^{2}$ + 2(a – 1)x + 2 is positive for all x if

$a^{2}$ – 1 > 0 and 4 $(a - 1)^{2} - 8 (a^{2} - 1)$ < 0

$\Rightarrow a^{2}$ – 1 > 0 and –4(a – 1)(a + 3) < 0

$\Rightarrow a^{2}$ – 1 > 0 and (a – 1)(a + 3) > 0

$\Rightarrow a^{2}$ > 1 and a < –3 or a > 1

$\Rightarrow$ a < –3 or a > 1

Suggest Corrections

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