If $(x-2)$ is a common factor of the expressions $x^2+a x+b$ and $x^2+c x+d$, then $\frac{b-d}{c-a}$ is…
If $(x-2)$ is a common factor of the expressions $x^2+a x+b$ and $x^2+c x+d$, then $\frac{b-d}{c-a}$ is equal to
$-2$
$-1$
$1$
$2$
Solution
Since, $(x-2)$ is a common factor of the expressions $x^2+a x+b$ and $x^2+c x+d$
$\begin{array}{rlrl}\Rightarrow & 2 a+b =2 c+d \\ \Rightarrow & b-d =2(c-a) \\ \Rightarrow & \frac{b-d}{c-a} =2\end{array}$
