If α,β,γ are the roots of x 3 +px 2 +qx+r=0, then ∑α 2 (β+γ) is A 3r+pq B 3r−pq C pq−3r D pq+r

 Question

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

A

3r+pq

B

3r−pq

C

pq−3r

D

pq+r

Medium

Solution

Verified by   GMS

Correct option is B)

Given: α,β,γ are the roots of x3+px2+qx+r=0

We have
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

                         =3r−pq