Evaluate the Discriminant for the Equation $- 8 a x ^ { 7 } \left( - 12 a x ^ { 5 } - 5 x ^ { 2 } + 6 a \right)$

Multiple Choice

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
- $- 8 a x ^ { 7 } \left( - 12 a x ^ { 5 } - 5 x ^ { 2 } + 6 a \right)$

A) $96 a ^ { 2 } x ^ { 35 } + 40 a x ^ { 14 } - 48 a ^ { 2 } x ^ { 7 }$
B) $96 a x ^ { 12 } + 40 a x ^ { 9 } - 48 a x ^ { 7 }$
C) $96 a ^ { 2 } x ^ { 12 } - 40 a x ^ { 9 } + 48 a ^ { 2 } x ^ { 7 }$
D) $96 a ^ { 2 } x ^ { 12 } + 40 a x ^ { 9 } - 48 a ^ { 2 } x ^ { 7 }$