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
B
1
C
1
D
2

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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