Let `lambda in R` . If the origin and the non-real roots of `2z^2+2z+lambda=0` form the three vertices of an equilateral triangle in the Argand lane, then `lambda` is

Options

A. 1
B. `(2)/(3)`
C. 2
D. -1

Answer

B

Explanation

`2z^(2)+2z+lambda=0`
Let the roots be `z_(1),z_(2)`. Then
`z_(1)+z_(2)=-1 and z_(1)z_(2)=(lambda)/(2)`
`0, z_(1),z_(2)` form an equilateral triangle.
`therefore z_(1)^(2) +z_(2)^(2)=z_(1)z_(2)`
`rArr (z_(1)+z_(2))^(2)=3z_(1)z_(2)`
`rArr 1 = 3(lambda)/(2)`
or `lambda = (2)/(3)`