Find the Zeros and Their Multiplicities $$f ( x ) = x ^ { 9 } + 10 x ^ { 8 } + 27 x ^ { 7 } + 20 x ^ { 6 } + 50 x ^ { 5 }$$

Multiple Choice

Find the zeros and their multiplicities. Consider using Descartes' rule of signs and the upper and lower
bound theorem to limit your search for rational zeros.
- $$f ( x ) = x ^ { 9 } + 10 x ^ { 8 } + 27 x ^ { 7 } + 20 x ^ { 6 } + 50 x ^ { 5 }$$

A) 0 (multiplicity 5) , 5 (multiplicity 2 ) and $\pm i \sqrt { 2 }$ (each multiplicity 1 )
B) 0 (multiplicity 5 ) , $- 5$ (multiplicity 2 ) and $\pm i \sqrt { 2 }$ (each multiplicity 1 )
C) 0 (multiplicity 5) , 5 (multiplicity 2 ) and $\pm 2 i$ (each multiplicity 1 )
D) 0 (multiplicity 5) , 5 (multiplicity 2 ) and $\pm \sqrt { 2 }$ (each multiplicity $1 )$