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Question

Let α,β are the roots of the equation 2x23x7=0, then the quadratic equation whose roots are αβ and βα is

A
14x2+37x14=0
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B
14x237x14=0
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C
14x237x+14=0
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D
14x2+37x+14=0
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Solution

The correct option is D 14x2+37x+14=0
2x23x7=0
From the given equation,
α+β=32, αβ=72
When the roots are,
αβ,βα
Sum of roots
αβ+βα=α2+β2αβ =(α+β)22αβαβ =94+772=3714
Product of roots
αβ×βα=1
Hence, required equation is
x2+3714x+1=014x2+37x+14=0

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