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If the sum of the roots of the quadratic...

If the sum of the roots of the quadratic equation `ax^2+bx+c=0` is equal to the sum of the squares of their reciprocals, show that `bc^2,ca^2,ab^2` are in Arithmetic Progression (AP). It is well known that if any three consecutive terms, form a sequence, are such ttiat the difference between any two consecutive terms is same' then they are in AP.

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