The value of b for which the equations x^2+b x-1=0, x^2+x+b=0 have one root in common is

Step-by-step solution

If a₁ x^2+b₁ x+c₁=0 and a₂ x^2+b₂ x+c₂=0 have a common real root, then aligned (a₁ c₂-a₂ c₁ )^2= (b₁ c₂- . & .b₂ c₁ ) & (a₁ b₂-a₂ b₁ ) aligned . array l x^2+b x-1=0 x^2+x+b=0 array have a common root. (1+b)^2= (b^2+1 )(1-b) b^2+2 b+1=b^2-b^3+1-b b^3+3 b=0 b (b^2+3 )=0 b=0, 3 i