Question

Given that $(x+1)$ is a common factor of $x^2+ax+b$ and $x^2+cx-d$, then

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

Answer 1

Answer: (B)

$a=b+c+d$

The two equations are
$x^2+ax+b=0$
$x^2+cx-d=0$
Since $(x+1)$ is their common root, $x=-1$ satisfies both the equations.
Substituting $x=-1$ in both the equations we get
$1-a+b=0$ ...(i)
$1-c-d=0$ ...(ii)
Since (i) and (ii) are equal to zero
$1-a+b=1-c-d$
$a=b+c+d$
Hence the answer is B.