find value of b

Let z₁ and z₂ be complex roots of 3z²+3z+b=0.If the origin,together with the points represented by z₁ and z₂ forms equilateral triangle,then find b.

2 Answers

b=1

Use these equations
z₁+z₂=-1 ... (i)
z₁z₂=b/3 ... (ii)
and

since z₁, z₂ and originn form an eq. triangle.
z₂=z₁e^Â±iÏ€/3 ....(iii)

(Either sign will give the same result... you can start with whatever sign you like)

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