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Let lambda in R . If the origin and the...

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 `1` b. `2/3` c. `2` d. `-1`

A

1

B

`(2)/(3)`

C

2

D

-1

Text Solution

Verified by Experts

The correct Answer is:
B
`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)`
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