The Characteristic Polynomial of a 5 × 5 Matrix Is $$\lambda ^ { 5 } + 17 \lambda ^ { 4 } + 72 \lambda ^ { 3 }$$

Multiple Choice

The characteristic polynomial of a 5 × 5 matrix is given below. Find the eigenvalues and their multiplicities.
- $$\lambda ^ { 5 } + 17 \lambda ^ { 4 } + 72 \lambda ^ { 3 }$$

A) 0 (multiplicity 1) , 8 (multiplicity 1) , 9 (multiplicity 1)
B) 0 (multiplicity $1 ) , - 9$ (multiplicity $1 ) , - 8$ (multiplicity 1 )
C) 0 (multiplicity 3) , 8 (multiplicity 1) , 9 (multiplicity 1)
D) 0 (multiplicity 3) , $- 9$ (multiplicity $1 ) , - 8$ (multiplicity 1 )