Let α, β and γ are the roots of the equation 2x^3+9x^2-27x-54=0. If α,β,γ are in geometric progression, then the value of α+β+γ=

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MARKS Content Team · Accepted Answer

Correct answer: (B) 21/2. Let, α=(β)/r and γ=βr α⋅β⋅γ=(β)/r⋅β⋅βr=54/2=27 ⇒β^3=27⇒β=3 α+β+γ=(β)/r+β+βr=-9/2 ⇒3/r+3+3r=-9/2 ⇒1/r+1+r=-3/2 ⇒2+2r+2r^2=-3r ⇒2r^2+5r+2=0 ⇒2r+1r+2=0⇒r=-1/2,-2 α=(β)/r=3/(-2)=(-3)/2 β=3 γ=βr=3-2=-6 α+β+γ=3/2+3+6=21/2

Let $α, β$ and $γ$ are the roots of the equation $2 x^{3} + 9 x^{2} - 27 x - 54 = 0 .$ If $α, β, γ$ are in geometric progression, then the value of $|α| + |β| + |γ| =$

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More Sequences and Series Questions

Let α, β and γ are the roots of the equation 2x3+9x2-27x-54=0. If α,β,γ are in geometric progression, then the value of α+β+γ=

Solution

More Sequences and Series Questions

Let $α, β$ and $γ$ are the roots of the equation $2 x^{3} + 9 x^{2} - 27 x - 54 = 0 .$ If $α, β, γ$ are in geometric progression, then the value of $|α| + |β| + |γ| =$