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Question

If αβ,α2=5α3,β2=5β3, then the equation whose roots are α/β & β/α is

A
x2+5x3=0
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B
3x2+12x+3=0
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C
3x219x+3=0
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D
None of these
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Solution

The correct option is D 3x219x+3=0
Given
α2=5α3
β2=5β3
So we can say roots of x25x+3=0 are α,β
α+β=5
αβ=3

Now, for equation whose roots areαβ and βα
Sum of the roots =αβ+βα=(α2+β2)αβ
=(α+β)22αβαβ
=2563=193
Product of roots = αβ×βα
=1
So, the required equation is
x2(sum of roots)x+product of roots=0
x2193x+1=0
3x219x+3=0

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