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Question

If α,β are the roots of equation a(x21)+2bx=0, then the equation whose roots are 2α1β & 2β1α is


A

bx2+6ax9b=0

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B

ax2+2bxa=0

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C

ax2+6bx+9a=0

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D

ax2+6bx9a=0

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Solution

The correct option is D

ax2+6bx9a=0


Given that α & β are the roots of the equation a(x21)+2bx=0.
α+β=2ba & αβ=1

We need to find the equation whose roots are 2α1β & 2β1α.

Sum of roots:
S=2α1β+2β1α
S=2(α+β)(1α+1β)

S=2(α+β)α+βαβ
S=4ba+2ba=6ba
S=6ba

Now, Product of Roots:
P=2(α1β)(2β1α)
P=4αβ22+1αβ
P=9

The required quadratic equation would be of the form:
x2Sx+P=0
x2(6ba)x9=0
ax2+6bx9a=0


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