Question

what two number multiply to 2 but add up to -2

Answer 1

$xy=2\\ x+y=-2\\\\ xy=2\\ x=-y-2\\\\ (-y-2)y=2\\ -y^2-2y=2\\ y^2+2y=-2\\ y^2+2y+1=-1\\ (y+1)^2=-1 \Rightarrow y\in \emptyset$

There are no such numbers in real numbers.