Find a polynomial of least degree with only real coefficients and having the given zeros.
-$2 - \mathrm { i } , - 6$
A) $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 20 x + 30$
B) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 19 x - 30$
C) $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 19 x + 30$
D) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 19 x + 24$

Question

Quizplus · Accepted Answer

For polynomials with real coefficients, complex roots appear in conjugate pairs. Thus, the zeros are $2 - i$, $2 + i$, and $-6$. The polynomial is $(x - (2-i))(x - (2+i))(x + 6)$. Simplifying gives $x^3 + 2x^2 - 19x + 30$.

Find a Polynomial of Least Degree with Only Real Coefficients 2−i,−62 - \mathrm { i } , - 62−i,−6

Find a Polynomial of Least Degree with Only Real Coefficients $2 - \mathrm { i } , - 6$