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Question

If α,β,γ are the roots of x3+px2+qx+r=0, then α2(β+γ) is

A
3r+pq
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B
3rpq
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C
pq3r
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D
pq+r
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Solution

The correct option is B 3rpq
As α,β,γ are the roots of x3+px2+qx+r=0
It gives
α+β+γ=p
αβ+βγ+γα=q
αβγ=r

Now,
α2(β+γ)=(α2β+α2γ)+(β2γ+β2α)+(γ2α+γ2β)
=(α+β+γ)(αβ+βγ+γα)3αβγ
=pq+3r
=3rpq

Hence, option B.

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