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Question

If α,β be the roots of x2+x+2=0 and γ,δ be the roots of x2+3x+4=0, then (α+γ)(α+δ)(β+γ)(β+δ) is equal to

A
18
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B
18
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C
24
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D
44
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Solution

The correct option is D 44

α+β=1,αβ=2,γ+δ=3,γδ=4

Now, (α+γ)(α+δ)(β+γ)(β+δ)

=(α2+(3)α+4)(β23β+4)

=(α23α+4)(β23β+4)

=(4α+2)(4β+2)

=4(2α1)(2β1)

=4(4αβ2α2β+1)

=4(8+2+1)=44


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