The correct option is B −i√3
Let α be the common root of given equations, then
α2+bα−1=0.......(1)
and α2+α+b=0.......(2)
Subtracting (2) from (1), we get
(b−1)α−(b+1)=0
or α=b+1b−1
Substituting this value of α in equation (1) , we get
(b+1b−1)2 +b(b+1b−1)−1=0
or b3+3b=0
⇒b=0,i√3,−i√3