Question

the polynomial with real coefficient whose zeros are -4, 1-i, 1+ is ...
a) x^3+6x^2+10x+8
b)x^3-2x^2-6x-8
c)x^3+2x^2-6x+8
d)x^3-6x^2+10x-8

Answer 1

\(\large {
x=\{4, 1-i, 1+ i\}\quad \\ \quad \\
\begin{cases}
x=4\to x-4=0\to {\color{brown}{ (x-4)}}=0\\
x=1-i\to x-1+i=0\to {\color{brown}{ (x-1+i)}}=0\\
x=1+i\to x-1-i=0\to {\color{brown}{ (x-1-i)}}=0
\end{cases}
\\ \quad \\
{\color{brown}{ (x-4)}}{\color{brown}{ (x-1+i)}}{\color{brown}{ (x-1-i)}}=0
\\ \quad \\
{\color{brown}{ (x-4)}}{\color{brown}{ (x-1+i)}}{\color{brown}{ (x-1-i)}}=\textit{original polynomial}
}\)