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Question

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


A
2
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B
1
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C
1
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D
2
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Solution

The correct option is D $$2$$
Given $$(x-2)$$ is a common factor of $$ x^{2}+ax+b$$ and $$ x^{2}+cx+d$$

$$\therefore x=2$$ is a root of $$ x^{2}+ax+b=0$$ and $$ x^{2}+cx+d=0$$

$$\therefore 4+2a+b=0, 4+2c+d=0$$

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

$$\Rightarrow 2(c-a)=b-d$$

$$\Rightarrow \dfrac{b-d}{c-a}=2$$

Mathematics

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