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Question

The ratio of the roots of the equation a1x2+b1x+c1=0 and a2x2+b2x+c2=0 are equal , then

A
(b1b2)2=a2c2a1c1
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B
(c1c2)2=b1c2c1b2
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C
(a1a2)2=(c1c2)2
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D
(b1b2)2=a1c1a2c2
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Solution

The correct option is D (b1b2)2=a1c1a2c2
As α,β are roots of a1x2+b1x+c1=0
And γ,δ are roots of a2x2+b2x+c2=0
αβ=γδαγ=βδ
α+βδ+γ=β(αβ+1)δ(γδ+1)=(βδ)2=αβγδ(α+β)2(γ+δ)2=(αβγδ)
(b1a1)2(b2a2)2=c1a1c2a2b21b22=a1c1a2c2

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