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Question

If α1, α2, α3..αn are the roots of xn+ax+b=0, then (α1α2)(α1α3)..(α1αn)=

A
nαn11
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B
a
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C
nαn11+a
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D
nαn11a
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Solution

The correct option is B nαn11+a
Since,α1, α2, α3..αn are the roots of xn+ax+b=0
(xα1)(xα2)(xα3).....(xαn)=xn+ax+b
(xα2)(xα3).....(xαn)=xn+ax+bxα1
limxα1(xα2)(xα3).....(xαn)=limxα1xn+ax+bxα1
applying L'Hospital's rule in RHS as it is of the form 00
(α1α2)(α1α3)..(α1αn)=limxα1nxn1+a1
(α1α2)(α1α3)..(α1αn)=nα1n1+a

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