Factorise a polynomial without given the equation

P(x) is an even monic polynomial of degree 4 with integer coefficients. One zero is 2i and the product of the zeros is -8. Factorise P(x) over R.

the answer is -2i, 2i, root 2, - root2

i know that if 2i is a root, then -2i is also another root, but I dont get how they got root 2 and - root 2

I can let the other roots be "a" and "b"

where ab = -2 (since product of roots is -8), however I don't understand how you could get root 2, - root 2 from that

Thanks (Rofl)