If α,β and γ are the roots of the equation x3+3x+2=0 and (α−β)(α−γ),(β−γ)(β−α),(γ−α)(γ−β) are the roots of equation y3−9y2−216=0 . Express y in terms of α.
α,β,γ are the roots of equation x3+3x+2=0 ___________(1)
Sum of the roots α+β+γ=−ba=0→β+γ=−α
Sum of the roots taking two at a time αβ+βγ+γα=ca=3
Product of the roots αβγ=−da=−2→βγ=−2α
We can take y = (α−β)(α−γ)=α2−αβ−αγ+βγ