lf α,β,γ are the roots of x3+ax+b=0, then the transformed equation having the roots (β−γ)2,(γ−α)2,(α−β)2 is obtained by taking x=
A
by+a
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B
2by+a
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C
3by+a
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D
4by+a
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Solution
The correct option is D3by+a As α,β,γ are roots of x3+ax+b=0 s1=α+β+γ=0s2=αβ+βγ+αγ=as3=αβγ=−b αβ+βγ+αγ=a⇒αβγ+βγ2+αγ2=aγ⇒γ2(α+β)=aγ−αβγ⇒−γ3=aγ+b⇒γ3=−aγ−b Let y=(α−β)2=(α+β)2−4αβ=γ2−4αβ ⇒yγ=γ3−4αβγ=−aγ−b+4b=3b−aγ ⇒γ(y+a)=3b⇒γ=3by+a⇒x=3by+a