Question

$\text{The value of}a\text{for which}$ $(a^2-1)x^2-(a-1)x+a^2-4a+3=0$ $\text{is an identity in}x$

• A. 1
• B. 1.0
• C. 01

Answer 1

Answer: (A), (B), (C)

Given $(a^2-1)x^2-(a-1)x+a^2-4a+3=0$
For this to be an identity in $x$, the coefficients of various powers of $x$ and constant term must be zero.

Put coefficient of $x^2=0$,
$\Rightarrow (a^2-1)=0$
$\Rightarrow (a+1)(a-1)=0$
$\Rightarrow a=-1,1$

Put coefficient of $x=0$,
$\Rightarrow (a-1)=0$
$\Rightarrow a=1$

Put constant term $=0$,
$\Rightarrow a^2-4a+3=0$
$\Rightarrow (a-1)(a-3)=0$
$\Rightarrow a=1,3$

Hence, the common value of $a$ is $1$.
$a=1$