Chapter 6.7, Problem 4CYP

To determine

To find: Polynomial function with least degree having zeros $-1$ and $1+2i$ .

Answer to Problem 4CYP

The required polynomial function is $x^2-2ix-\left(1+2i\right)=y$ .

Explanation of Solution

Given information:

Zeros of required polynomial equation are $-1$ and $1+2i$ .

Given that, zeros of required polynomial function are $-1$ and $1+2i$ .

That means these are solution of required polynomial equation,

  $\begin{array}{l}x=-1\\ \\ x+1=0\end{array}$

  $\begin{array}{l}x=1+2i\\ \\ x-1-2i=0\end{array}$

So, the required equation is,

  $\begin{array}{l}\left(x+1\right)\left(x-1-2i\right)=y\\ \\ x^2-x-2ix+x-1-2i=y\\ \\ x^2-2ix-\left(1+2i\right)=y\end{array}$

The required polynomial function is $x^2-2ix-\left(1+2i\right)=y$ .