Question

If the equations $x^2+bx+c=0$ and $x^2+cx+b=0(b\ne c)$ have a common root, then :

• A. None
• B. $b+c+1=0$
• C. $b+c=0$
• D. $b+c=1$

Answer 1

The correct option is B

$b+c+1=0$

If $\alpha$ is the common root, then ${\alpha }^2+b\alpha +c=0$ and ${\alpha }^2+c\alpha +b=0$

Subtracting, $(b-c)\alpha +c-b=0$
$\Rightarrow \alpha =1$

$\therefore 1+b.1+c=0i.e.,b+c+1=0$