Find a polynomial with integer coefficients, with leading coefficient 1, degree 5, zeros i and 8-i, and passing through the origin

Question

tkhunny · Answer

What's your plan?  With REAL integer coefficients (which the problem statement didn't quite say explicitly), what are the other two zeros to go along with i and 8-i?

anonymous · Answer

Find a polynomial with integer coefficients, with leading coefficient 1, degree 5, zeros i and 4- i, and passing through the origin.

tkhunny · Answer

Is the problem statement hopping around?  I ask again, what's your plan?  You need three more zeros.  Where are you going to get them?

anonymous · Answer

there is one at the origin but thats all the question ask me

tkhunny · Answer

You are to use your knowledge to come up with the other three.  You found the one at the Origin.  That is good.  What about the other two.  They are easily found if you put together the two facts.

1) i and 4-i are zeros.
2) The coefficients are REAL.