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Q.

If α,β,γ are different from 1 and the roots of ax3+bx2+cx+d=0 and a≠0 , α-ββ-γγ-α=152 and if α1-αβ1-βγ1-γαβγα2β2γ2=pda+b+c+d . Then greatest integer less than |p| is

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answer is 7.

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Detailed Solution

Δ=αβγ(1−α)(1−β)(1−γ)1111−α1−β1−γα(1−α)β(1−β)γ(1−γ)  R1→R1-R2,=αβγ(1−α)(1−β)(1−γ)111αβγα1-α β1-β γ1-γ   R2→R2-R3 αβγ(1−α)(1−β)(1−γ)111αβγα2β2γ2 =αβγ(α−β)(β−γ)(γ−α)(1−α)(1−β)(1−γ)=−da×152a+b+c+da=−152da+b+c+d|p|=7.50
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