If - - Y are the roots of x3-1 x-m-0- then the value of -3-3-3 is

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

Relation between Roots and Coefficients for Quadratic

If α, β, Y ar...

Question

If $α, β, γ$ are the roots of $x^{3} + l x + m = 0$ , then the value of $α^{3} + β^{3} + γ^{3}$ is

0

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

3 l

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

- 3 m

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

- 3 l

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

Open in App

Solution

The correct option is C $- 3 m$
$α + β + γ = 0$ ,
$α β + β γ + γ α = l$ ,
$α β γ = - m$
and we know that
$α^{3} + β^{3} + γ^{3} - 3 α β γ = (α + β + γ) (α^{2} + β^{2} + γ^{2} - α β - β γ - α γ)$
$∵ α + β + γ = 0$
$∴ α^{3} + β^{3} + γ^{3} = 3 α β γ = - 3 m$

Suggest Corrections

Similar questions

Q. If

α, β, γ

are the roots of

x^{3} + l x + m = 0

, then the value of

α^{3} + β^{3} + γ^{3}

Q. If

α, β, γ

are the roots of the cubic

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

, then value of

\frac{1}{α^{3} + β^{3} + 6} + \frac{1}{β^{3} + γ^{3} + 6} + \frac{1}{γ^{3} + α^{3} + 6}

is equal to

If α, β, γ are the roots of $x^{3}$ + 3x + 2 = 0. Find the equation whose roots are $α^{3}$ , $β^{3}$ , $γ^{3}$ . Also find the value of $α^{3}$ + $β^{3}$ + $γ^{3}$ - 3αβγ.

Q. If

α, β, γ

are the roots of the equation

x^{3} + 4 x + 2 = 0

, then

α^{3} + β^{3} + γ^{3} =

Q. lf

α, β, γ

are the roots of

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

then

α^{3} + β^{3} + γ^{3} =

Join BYJU'S Learning Program

If α,β,γ are the roots of x3+lx+m=0, then the value of α3+β3+γ3 is

The correct option is C −3mα+β+γ=0, αβ+βγ+γα=l, αβγ=−m and we know that α3+β3+γ3−3αβγ=(α+β+γ)(α2+β2+γ2−αβ−βγ−αγ) ∵α+β+γ=0 ∴α3+β3+γ3=3αβγ=−3m

If $α, β, γ$ are the roots of $x^{3} + l x + m = 0$ , then the value of $α^{3} + β^{3} + γ^{3}$ is

The correct option is C $- 3 m$
$α + β + γ = 0$ ,
$α β + β γ + γ α = l$ ,
$α β γ = - m$
and we know that
$α^{3} + β^{3} + γ^{3} - 3 α β γ = (α + β + γ) (α^{2} + β^{2} + γ^{2} - α β - β γ - α γ)$
$∵ α + β + γ = 0$
$∴ α^{3} + β^{3} + γ^{3} = 3 α β γ = - 3 m$