What is a polynomial that has the roots: 3 and 5-i and also crosses the origin with integer coefficients? question
What is a polynomial that has the roots: 3 and 5-i and also crosses the origin with integer coefficients?
My thoughts
on my first instinct, i wrote this:

$(x-(5-i))(x+(5-i))(x-3)(x)$

But then i've realized that when you factor out the complex parts, you dont get integer coefficients so I was really confused if this is even possible

Note that the conjugate of $5-i$ is $5+i$. 
So,$$(x-5+i)(x-5-i)(x-3)x=x(x-3)(x^2-10x+26)$$
Is the simplest polynomial that meets the conditions. 
