Hey guys I got stuck halfway through a problem, here's what I have so far:

Q: Find a quadratic function, with integer coeff, that has a root of 6 - i.

So I know that if 6 - i is a root, it's conjugate, 6 + i must also be a root. But, (x + 6 - i)(x - 6 + i) yields x^2 + 12i - 35, which doesn't have integer coefficients.

I'm stuck on how to get integer coefficients :(

Thanks so much in advance!

Question

Hey guys I got stuck halfway through a problem, here's what I have so far:

Q: Find a quadratic function, with integer coeff, that has a root of 6 - i. 

So I know that if 6 - i is a root, it's conjugate, 6 + i must also be a root. But, (x + 6 - i)(x - 6 + i) yields x^2 + 12i - 35, which doesn't have integer coefficients. 

I'm stuck on how to get integer coefficients :(

Thanks so much in advance!

mjdennis · Answer

You are correct that you need to go with the complex conjugate.  Try that multiplication again -- because the 'i' term should have gone away -- while I take a look at the problem

cocoacat · Answer

Oh I see what I did wrong! It should be (x - 6 + i)(x - 6 - i)
I multiplied the wrong thing XD

cocoacat · Answer

Thanks so much for your help!

mjdennis · Answer

OK, first problem is farther back.  You wrote your terms wrong.  
If 3 is a root, then (x-3) is the matching term.  You used plus signs... yeah, I see you got it.

mjdennis · Answer

De nada.