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=γδ⇒αγ=βδ ⇒α+βδ+γ=β(αβ+1)δ(γδ+1)=√(βδ)2=√αβγδ⇒(α+β)2(γ+δ)2=(αβγδ) ⇒(−b1a1)2(−b2a2)2=c1a1c2a2∴b21b22=a1c1a2c2