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Question

If α1,α2, α3, αn are the roots of the equation (xβ1)(xβ2)(xβn)=A and if the equation having β1, β2, β3, βn as the roots is (xα1)(xα2)(xαn)=k, then k=

A
A
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B
A
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C
Aα1α2αn
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D
Aα1α2αn
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Solution

The correct option is B A
As α1,α2,α3,αn are roots of

(xβ1)(xβ2)...(xβn)=A

Then

(xβ1)(xβ2)...(xβn)A=(xα1)(xα2)...(xαn) (1)

Now as β1,β2,β3,βn are roots of

(xα1)(xα2)...(xαn)k=(xβ1)(xβ2)...(xβn)

(xα1)(xα2)...(xαn)k=(xα1)(xα2)...(xαn)+A [from (1)]

k=A

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