Question

For $a\ne b$, if the equations $x^2+ax+b$ and $x^2+bx+a=0$ have a common root, the value of $(a+b)$ is

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is A $-1$

$x^2+ax+b=0$ ...(i)
$x^2+bx+a=0$ ...(ii)
Subtracting (ii) from (i), we get
$(a-b)x+(b-a)=0$
$(a-b)x-(a-b)=0$
$x=1$ is the common root.
Substituting in any one of the equation, we get
$a+b=-1$.