If the sum of the roots of the quadratic equation is equal to the sum of the squared of their reciprocals then , are in:
Find the form of reciprocal.
Let us consider that and are the roots of the given equation .
So,
and
From the given condition, The squares of their reciprocals are equal to the sum of the roots of the quadratic equation.
So,
As we know that, Harmonic progression is a progression formed by taking the reciprocals of an Arithmetic progression.
The first term of a HP is .
If the H.P. be as , , then corresponding A. P. is .
Hence, the reciprocal are in Harmonic progression (H. P.).