Question

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

• A. $-2$
• B. $-1$
• C. $1$
• D. $2$

Answer 1

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 $x^2+cx+d=0$

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

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

$\Rightarrow 2(c-a)=b-d$

$\Rightarrow \frac{b-d}{c-a}=2$