If x = 3i is a root of the polynomial P(x) which has real coefficients, then what other root is guaranteed? (

Question

zepdrix · Answer

COMPLEX roots always appear as conjugate pairs.
Conjugate pairs look like this:
(a-b)(a+b)

If x=3i is a root, then (x-3i) is a factor of this polynomial.
What would the other factor be? :)
(x-3i)(a+b)

What is the a+b? :D

anonymous · Answer

lol im still confused.

zepdrix · Answer

Mmmm maybe I'm making it more complicated than it needs to be. hehe.

zepdrix · Answer

So look at the a and b.
The terms should be the same as one another, just with a different sign in between.
(a-b)(a+b)
(x-2)(x+2)

So if this polynomial has a root x=3i, which we can rewrite as (x-3i),
(x-3i)(  +  )

Remember, complex roots always come with a buddy, their twin brother, but he's the evil twin :O the same... just with a different sign.

zepdrix · Answer

So what goes in the second set of brackets? :D around the plus sign.

zepdrix · Answer

Ok just in case I'm confusing you more :D
(x-3i)(x+3i)

(x+3i) should also be a factor of this polynomial, meaning that x=-3i is your other guaranteed root.