Question

If $(x+2)$ is the HCF of $x^2+ax+b$ and $x^2+cx+d$ ($a\ne c$ and $b\ne d$), then which one of the following is correct?

• A. $a+c=b+d$
• B. $2a+b=2c+d$
• C. $b+2c=2a+d$
• D. $b-2c=2a-d$

Answer 1

The correct option is C $b+2c=2a+d$

As $(x+2)$ is HCF of 2pdy $\Rightarrow x=-2$ is root of

these eq${}^n$.

$\Rightarrow (-2{)}^2-2a+b=0$ & $(-{21}^2-2c+d)=0$

$\Rightarrow b-2a+4=\mathrm{0...}\left(1\right)$ & $d-2c+4=\mathrm{0...}\left(2\right)$

$\therefore$ from (1) & (2)

$b+2c=2a+d$