Find an Nth Degree Polynomial Function with Real Coefficients Satisfying $\mathrm { n } = 4 ; 2 \mathrm { i } , 7$

Multiple Choice

Find an nth degree polynomial function with real coefficients satisfying the given conditions.
- $\mathrm { n } = 4 ; 2 \mathrm { i } , 7$ , and $- 7$ are zeros; leading coefficient is 1

A) $f ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196$
B) $f ( x ) = x ^ { 4 } + 4 x ^ { 3 } - 45 x ^ { 2 } - 196$
C) $f ( x ) = x ^ { 4 } + 4 x ^ { 2 } - 196$
D) $f ( x ) = x ^ { 4 } + 4 x ^ { 2 } - 7 x - 196$