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

• A

  $-2$
• B

  $-1$
• C

  $1$
• Correct answer
  D

  $2$

Solution

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

Hence, the correct answer is option: 'D'.