Question

$\left(x-2\right)$ is a common factors of the expressions $x^2+ax+b$ and $x^2+ex+d$, then $\frac{b-d}{c-a}=?$

Answer 1

$(x-2)$ common factor of $x^2+ax+6$ $\&$ $x^2+ex+d.$

$\therefore 2$ will be zero of both expression

$\Rightarrow {\left(2\right)}^2+2\left(2\right)+b=0$ $2a+b=-4$

${\left(2\right)}^2+c\left(2\right)+d=0$ $2c+d=-4$

$\therefore 2a+b=2c+d$

$\Rightarrow 2(c-a)=(b-d)$

$\Rightarrow \frac{(b-d)}{(c-a)}=2$

Hence, the answer is $2.$