Let λ∈R,  the origin and the non-real roots of 2z2+2z+λ=0  from the three vertices of an equilateral triangle in the Argand plane then λ  is

2z2+2z+λ=0 Let the roots be z1,  z2.  Then, z1+z2=−1  and z1z2=λ20,  z1,  z2  form an equilateral triangle.   if z1,z2,z3  form an equilateral triangle then  z12+z22+z32=z1z2+z2z3+z3z1∴  z12+z22=z1z2⇒  (z1+z2)2=3z1z2⇒  1=3λ2⇒  λ=23