Question

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

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

Answer 1

The correct option is C

b + c + 1 = 0

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

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

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