If the equations x 2 + b x - 1 = 0 and x 2 + x + b = 0 have a common root different from - 1 , then b is equal to :

Step-by-step solution

Let common root be x x 2 + b x - 1 = 0 ... 1 x 2 + x + b = 0 ... 2 1 - 2 , we get x = b + 1 b - 1 Put x in Equation 1 , we get b + 1 b - 1 2 + b + 1 b - 1 + b = 0 ⇒ b + 1 2  +  b + 1   b - 1 + b b - 1 2 = 0 ⇒ b 2 + 1 + 2 b + b 2 - 1 + b b 2 - 2 b + 1 = 0 ⇒ 2 b 2 + 2 b + b 3 - 2 b 2 + b = 0 ⇒   b 3 + 3 b = 0 ⇒    b b 2 + 3 = 0 ⇒ b = 0 or b 2 = - 3 When b = 0 then common root x = - 1 But the given common root x ≠ - 1 ∴  b 2 =   -