Question

If $x-a$ is factor of both $p\left(x\right)=x^2-2x+1$ and $q\left(x\right)=x^2-3x+2$, what is the value of a?

• A. 2
• B. 3
• C. 1
• D. 4

Answer 1

The correct option is C 1

$\because$ $x-a$ is a factor of $p\left(x\right)$ and $q\left(x\right)$, we have
$p\left(a\right)=0andq\left(a\right)=0$

$\Rightarrow$ $p\left(a\right)=a^2-2a+1=0$
Also,
$\Rightarrow$ $q\left(a\right)=a^2-3a+2=0$

$\because$ p(a) = 0 = q(a)

We have, $p\left(a\right)=q\left(a\right)$

$\Rightarrow a^2-2a+1=a^2-3a+2$
$\Rightarrow -2a+1=-3a+2$
$\Rightarrow -2a+3a=2-1$
$\Rightarrow a=1$