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Quadratic Identity

If P2-1 x2+P-...

Question

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

1

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2

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- 1

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0

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Solution

The correct option is A $1$
Conditions:
$P^{2} - 1 = 0 \Rightarrow P = \pm 1 \dots (1) P - 1 = 0 \Rightarrow P = 1 \dots (2) P^{2} - 4 P + 3 = 0 \Rightarrow (P - 3) (P - 1) = 0 \Rightarrow P = 1, 3 \dots (3)$
From equation $(1), (2)$ and $(3)$ ,
$P = 1$

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