You visited us 1 times! Enjoying our articles? Unlock Full Access!

Equation of Circle in Complex Form

α, β, γ are r...

Question

$α, β, γ$ are roots of $x^{3} - 2 x^{2} - x + 2 = 0$ . Centroid of triangle with vertices
$(α, β, γ), (β, γ, α), (γ, α, β)$ is

(- \frac{2}{3}, \frac{2}{3}, - \frac{2}{3})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(- \frac{2}{3}, \frac{1}{3}, \frac{2}{3})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(\frac{2}{3}, \frac{2}{3}, \frac{2}{3})

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(\frac{4}{3}, \frac{2}{3}, \frac{2}{3})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $(\frac{2}{3}, \frac{2}{3}, \frac{2}{3})$
$α + β + γ = 2$
centroid $= (\frac{α + β + γ}{3}, \frac{β + γ + α}{3}, \frac{γ + α + β}{3}) = (\frac{2}{3}, \frac{2}{3}, \frac{2}{3})$

Suggest Corrections

Similar questions

α, β, γ

x^{3} + 2 x - 3 = 0

\frac{α}{β} + \frac{β}{α}, \frac{β}{γ} + \frac{γ}{β}, \frac{γ}{α} + \frac{α}{γ}

x =

α, β, γ

x^{3} + 3 x^{2} + 2 = 0

\frac{α}{β + γ}, \frac{β}{γ + α}, \frac{γ}{α + β}

α, β, γ

x^{3} + 2 x^{2} - 3 x - 1 = 0

α^{- 2} + β^{- 2} + γ^{- 2}

α, β, γ

x^{3} + x^{2} + 2 x + 3 = 0

f (x) = 0

α + β, β + γ, γ + α

f (x) =

If α, β, γ are the roots of the equation $x^{3} + 4 x + 1 = 0$ ,then $(α + β)^{- 1} + (β + γ)^{- 1} + (γ + α)^{- 1} =$

Join BYJU'S Learning Program