Question

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

• A. $2$
• B. $-1$
• C. $1$
• D. $0$

Answer 1

The correct option is C $1$

Given expression is $(p^2-1)x^2+(p-1)x=0$
Condition for the given expression to be an identity is that all the coefficients must be zero.

$\Rightarrow p^2-1=0\text{and}p-1=0\Rightarrow p=\pm 1\cdots \left(1\right)\text{and}p=1\cdots \left(2\right)$

From equations $\left(1\right)\text{and}\left(2\right)$, the common value is taken
$\Rightarrow p=1$