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Question: Answered & Verified by Expert
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
MathematicsQuadratic EquationJEE Main
Options:
  • A $-2$
  • B $-1$
  • C $1$
  • D $2$
Solution:
2988 Upvotes Verified Answer
The correct answer is: $2$
Since, $(x-2)$ is a common factor of the expressions $x^2+a x+b$ and $x^2+c x+d$


$\begin{array}{rlrl}\Rightarrow & 2 a+b =2 c+d \\ \Rightarrow & b-d =2(c-a) \\ \Rightarrow & \frac{b-d}{c-a} =2\end{array}$

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