Answer
$$\color{blue}{ f(x)= x^2-14x+53 }$$
Work Step by Step
We are given zeros and asked to write a polynomial function.
If $ 7-2i $ is a zero, then
$n +7-2i =0$
$n -2i = -7 $
$n= -7 +2i $
So our factor is $\bf{(x -7 +2i )}$
because when $x= 7-2i $, $(x -7 +2i )=0$
If $ 7+2i $ is a zero, then
$n 7+2i =0$
$n +2i = -7 $
$n= -7-2i $
So our factor is $\bf{(x -7-2i )}$
because when $x= 7+2i $, $(x -7-2i )=0$
So our function is:
$f(x)= (x -7 +2i )(x -7-2i ) $
$f(x)= (x^2-7x-2ix-7x+49+14i+2ix-14i-4i^2) $
$f(x)= (x^2-14x+49-4i^2) $
Recall that $i^2=-1$
$f(x)= (x^2-14x+49-4(-1)) $
$f(x)= (x^2-14x+49+4) $
$$\color{blue}{ f(x)= x^2-14x+53 }$$