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Question

If α,β,γ are the roots of x3+3x2+4x+5=0 , then which of the following is/ are true.

A
α=3
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B
β2γ2=14
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C
1α=45
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D
α2=1
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Solution

The correct option is D α2=1
α+β+γ=3αβ+βγ+γα=4,αβγ=5

1α=αβ+βγ+γααβγ =45

α2=(α+β+γ)22(αβ+βγ+γα) =98=1

β2γ2=(αβ+βγ+γα)22αβγ(α+β+γ) =162(5)(3) =14

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