Find a Polynomial of Least Degree with Only Real Coefficients $3 + \sqrt { 2 } , 3 - \sqrt { 2 }$

question 163

Multiple Choice

Find a polynomial of least degree with only real coefficients and having the given zeros.
- $3 + \sqrt { 2 } , 3 - \sqrt { 2 }$ , and 2

• A) \(f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 19 x - 14\)
• B) \(f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 14\)
• C) \(f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 16\)
• D) \(f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 19 x - 14\)