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If alpha,beta gamma are zeroes of cubic ...

If `alpha,beta gamma` are zeroes of cubic polynomial `x^(3)+5x-2`, then find the value of `alpha^(3)+beta^(3)+gamma^(3)`.

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The correct Answer is:
N/a
`alpha+beta+gamma=(-b)/(a)=-(0)/(1)=0" "`(coefficient of `x^(2)`is 0)
`alphabeta+beta gamma+gamma alpha=(c )/(a)=(5)/(1)=5, alphabetagamma=-(d)/(a)=(-(-2))/(1)=2" "` .......(i)
Since, `alpha+beta+gamma=0`
`:. alpha^(3)+beta^(3)+gamma^(3)=3alphabetagamma=3(2)=6 " " `[from (1)] Ans.
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