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Cube Numbers

If a2-1x2+a...

Question

If $(a^{2} - 1) x^{2} + (a - 1) x + a^{2} - 4 a + 3 = 0$ be an identity in $x$ , then the value of $a$ .

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Solution

The correct option is B $1$
$(a^{2} - 1) x^{2} + (a - 1) x + a^{2} - 4 a + 3 = 0$
for this to be an identity in $x$ ,
$a^{2} - 1 = 0$
$a - 1 = 0$
$a^{2} - 4 a + 3 = 0$
$∴ a = \pm 1$ or $a = 1$ or $a = 1, 3$ .....(i)
$∴$ taking intersection of (i) we get
$a = 1$

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