If - - - be the roots of the equation 2x3 - 3x2 - 12x - 3 - 0 and A - - - B - - - C- - - represent vertices of a triangle ABC then the centroid of the triangle lies upon the line

The correct option is C x = y = zLet f(x) = 2x^3+3x^2 12x+3 ⇒ f(x) = 0 has three real roots (α, β, γ) ⇒α+β+ γ = 3/2 ∴ Centroid ...

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

Quadratic Formula

If α, β, γ ...

Question

If $α, β, γ$ be the roots of the equation $2 x^{3} + 3 x^{2} - 12 x + 3 = 0$ and $A (α, β, γ), B (β, γ, α) C (γ, α, β)$ represent vertices of a triangle ABC then the centroid of the triangle lies upon the line

x = y = z

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

x = 2y = 3z

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

x = - 2y =3z

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

x =y = - 2z

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

Open in App

Solution

Suggest Corrections

Similar questions

α, β, γ

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

(α, β, γ), (β, γ, α), (γ, α, β)

α, β, γ

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

(α, \frac{1}{α})

(β, \frac{1}{β})

(γ, \frac{1}{γ})

α, β, γ

x^{3} - 12 x^{2} + 44 x - 48 = 0.

A (α, \frac{1}{α}),

B (β, \frac{1}{β})

C (γ, \frac{1}{γ}),

△ A B C

α, β

γ

x^{3} - x - 1 = 0

\frac{1 + α}{1 - α} + \frac{1 + β}{1 - β} + \frac{1 + γ}{1 - γ}

α, β

γ

{2 x}^{3} + x^{2} - 13 x + 6

α β γ

Join BYJU'S Learning Program