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) $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } - 4$

Question

Quizplus · Accepted Answer

The polynomial with the given zeros is $f(x) = (x - (1 - \sqrt{3}))(x - (1 + \sqrt{3}))(x - (1 + i))(x - (1 - i))$. Expanding this product gives the polynomial $f(x) = x^4 - 4x^3 + 4x^2 - 4$.

Find a Polynomial of Least Degree with Only Real Coefficients 1−3,1+31 - \sqrt { 3 } , 1 + \sqrt { 3 }1−3​,1+3​

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