A value of b for which the equations x2+bx−1=0 and x2+x+b=0 have one root in common, is

We know that, if a1x2+b1x+c1=0 and a2x2+b22x+c2=0  have a common real root, then a1c2−a2c12=b1c2−b2c1a1b2−a2b1 then a1c2−a2c12=b1c2−b2c1a1b2−a2b1⇒(1+b)2=b2+1(1−b)⇒b2+2b+1=b2−b3+1−b⇒b3+3b=0⇒bb2+3=0⇒b=0,±i3