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Question

If and β are roots of x2 + ax - b = 0 and γ, δ​ arethe roots of x2 + ax + b = 0, then (α-γ) (β-δ) (α-δ) (β-γ)


A

4b2

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B

b

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C

2b

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D

2b2

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Solution

The correct option is A

4b2


α+β= -a , αβ= -b , γ+δ=-a γδ=b

therefore (α-γ) (β-δ) (α-δ) (β-γ)

=[ αβ-(α+β)γ+γ2][αβ-(α+β)δ+δ2]

(-b+aγ+γ2)(-b+aδ+δ2)

=(-b-b)(-b-b)=4b2


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