Question

if α and β are roots of quadratic equations 2x²-3x+1=0, then find the equation whose roots are 2α/β and 2β/α

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Answer 1

Answer:

α+β=

2

3

And

α.β=−3

Therefore,

α

2

+β

2

=(α+β)

2

−2αβ

=

4

9

+6

=

4

33

Hence, the equation will be

x

2

−(

4

33

+4)x+(9+2(

4

33

+4)=0

4x

2

−49x+118=0.