If the sum of the roots of the quadratic equation $ax^2 +bx +c+0$ is equal to sum of the squares of the reciprocals then $b^2 /ac +bc/a^2$ is equal to?
What I tried
I equated the sum of the roots and the sum of their reciprocals after which i got a relation saying that either the sum of the roots must be equal to zero or the multiple of the roots shall be equal to -1 for the equation to hold true.
Hint...you should be able to get the sum of the squares of the reciprocals as $$\frac{b^2-2ac}{c^2}$$ and the result will follow from this...
Can you finish?