Find a Polynomial of Least Degree with Only Real Coefficients $1 - \sqrt { 3 } , 1 + \sqrt { 3 }$

question 339

Multiple Choice

Find a polynomial of least degree with only real coefficients and having the given zeros.
- $1 - \sqrt { 3 } , 1 + \sqrt { 3 }$ , and $1 + i$

• A) \(f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 4 x ^ { 2 } - 4\)
• B) \(f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 4 x ^ { 2 } - 4\)
• C) \(f ( x ) = x ^ { 4 } + 3 x ^ { 3 } + 4 x ^ { 2 } - 1\)
• D) \(f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } - 4\)