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Question

If (α,β),(β,γ),(γ,α) are respectively the roots of x22px+2=0;x22qx+3=0;x22rx+6=0 where α,β,γ are all positive, then the value of p+q+r is

A
1
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B
2
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C
0
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D
6
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Solution

The correct option is D 6
(α,β),(β,α) and (γ,α) are roots of x22px+2=0, x22qx+3=0 &x22rx+6=0 respectively
So,
α+β=2pi
β+γ=2qii
γ+α=2riii
αβ=2iv
βγ=3v
γα=6vi
iv×v
=αβ2γ=6
β2(6)=6
β2=1
β±1
γ=±3
α=±2
p+q+r=α+β2+β+γ2+γ+α2
From i,ii, and iii
=2(α+β+γ)2
=2+1+3
=6

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