If $(x - 2)$ is a common factor of the expressions $x^{2} + ax + b$ and $x^{2} + cx + d$, then $\frac{b - d}{c - a}$ is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
Since, $(x - 2)$ is a commom factor of the expressions $x^{2} + ax + b$ and $x^{2} + cx + d$
$\Rightarrow \ \ \ 4 + 2a + b = 0$ ...(i)
And $4 + 2c + d = 0$ ...(ii)
$\Rightarrow \ \ \ \ 2a + b = 2c + d$
$\Rightarrow \ \ \ b - d = 2(c - a)$
$\Rightarrow \ \ \ \frac{b - d}{c - a} = 2$

Q. If $(x - 2)$ is a common factor of the expressions $x^{2} + ax + b$ and $x^{2} + cx + d$, then $\frac{b - d}{c - a}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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