You can put this solution on YOUR website! A key to this problem is to understand that if "r" is a root, then (x-r) is a factor. (Think about it. If x = r then x-r = 0. And if x-r =0 then the product of anything with (x-r) as a factor will be zero!)
Now let's think about your problem. If we want two roots which are negatives of each other, let's call them r and -r. So we want (x-r) and (x-(-r)) to be factors. And what does it look like if we multiply (x-r) and (x-(-r))?
Notice that there is no "x" term. This means that we need a quadratic with no x term in order to have roots that are negatives of each other.
So in , what value of "m" will make the middle term "disappear"? Answer: 0.
(