Find All of the Real Zeros of the Function $$f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 2 x ^ { 2 } + 36 x - 48$$

Multiple Choice

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
- $$f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 2 x ^ { 2 } + 36 x - 48$$

A) 4 (rational) , 2 (rational) , $\sqrt { 6 }$ (irrational) , and $- \sqrt { 6 }$ (irrational)
B) $- 4$ (rational) , $- 2$ (rational) , $2 + \sqrt { 6 }$ (irrational) , and $2 - \sqrt { 6 }$ (irrational)
C) $- 4$ (rational) , $- 2$ (rational) , $\sqrt { 6 }$ (irrational) , and $- \sqrt { 6 }$ (irrational)
D) 4 (rational) , 2 (rational) , $2 + \sqrt { 6 }$ (irrational) , and $2 - \sqrt { 6 }$ (irrational)