Question

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

• A. $1$
• B. $2$
• C. $-1$
• D. $0$

Answer 1

The correct option is A $1$

Conditions:
$P^2-1=0\Rightarrow P=\pm 1\cdots \left(1\right)P-1=0\Rightarrow P=1\cdots \left(2\right)P^2-4P+3=0\Rightarrow (P-3)(P-1)=0\Rightarrow P=1,3\cdots \left(3\right)$
From equation $\left(1\right),\left(2\right)$ and $\left(3\right)$,
$P=1$