Solve this following
Question:

If $m$ is chosen in the quadratic equation $\left(m^{2}+1\right)$ $x^{2}-3 x+\left(m^{2}+1\right)^{2}=0$ such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :-

1. $8 \sqrt{3}$

2. $4 \sqrt{3}$

3. $10 \sqrt{5}$

4. $8 \sqrt{5}$

Correct Option: , 4

Solution: