Find a polynomial of least degree with only real coefficients and having the given zeros.
-$5 + 4 i$ and $5 - 4 i$
A) $f ( x ) = x ^ { 2 } - 10 x + 9$
B) $f ( x ) = x ^ { 2 } + 41$
C) $f ( x ) = x ^ { 2 } + 10 x + 41$
D) $f ( x ) = x ^ { 2 } - 10 x + 41$

Question

Quizplus · Accepted Answer

The polynomial of least degree with real coefficients that has the zeros $5 + 4i$ and $5 - 4i$ can be found by using the fact that if $a + bi$ is a root, then its complex conjugate $a - bi$ is also a root. The polynomial is obtained by multiplying $(x - (5 + 4i))(x - (5 - 4i))$, which simplifies to $x^2 - 10x + 41$.

Find a Polynomial of Least Degree with Only Real Coefficients 5+4i5 + 4 i5+4i

Find a Polynomial of Least Degree with Only Real Coefficients $5 + 4 i$