If λ ∈ R such that the origin and the non-real roots of the equation 2 z 2 + 2 z + λ = 0 form the vertices of an equilateral triangle in the argand plane, then 1 λ is equal to

Step-by-step solution

Let, z 1 and z 2 are roots of the equation 2 z 2 + 2 z + λ = 0 ⇒ z 1 + z 2 = - 1   and   z 1 z 2 = λ 2 If 0 ,   z 1   &   z 2 form an equilateral triangle, then z 1 2 + z 2 2 = z 1 z 2 ⇒ z 1 + z 2 2 = 3 z 1 z 2 ⇒ - 1 2 = 3 λ 2 ⇒ 1 λ = 3 2 = 1 . 5