If - - - - are the roots of x3-lx-m-0- then the value of -3-3 - -3 is

Α + β + γ = 0, αβ + βγ + γα =l, αβγ = m and we know that α^3+β^3+γ^3 3 αβγ =(α + β + γ)(α^2+β^2+γ^2 nbsp; αβ βγ αγ) ∵α + β + γ =0 ∴α^3+β^3+γ^3 = 3 αβγ = ...

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Standard XII

Mathematics

Relation between Roots and Coefficients for Quadratic

If α , β, γ a...

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

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3 l

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- 3 m

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- 3 l

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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
$α^{3} + β^{3} + γ^{3} - 3 α β γ = (α + β + γ) (α^{2} + β^{2} + γ^{2} - α β - β γ - α γ)$
$∵ α + β + γ = 0$
$∴ α^{3} + β^{3} + γ^{3} = 3 α β γ = - 3 m$

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If α, β, γ are the roots of cubic equation a $x^{3}$ + cx = 0. Find the value of $α^{3}$ + $β^{3}$ + $γ^{3}$ .

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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
$α^{3} + β^{3} + γ^{3} - 3 α β γ = (α + β + γ) (α^{2} + β^{2} + γ^{2} - α β - β γ - α γ)$
$∵ α + β + γ = 0$
$∴ α^{3} + β^{3} + γ^{3} = 3 α β γ = - 3 m$