SOLUTION: Find the value of 'm' such that the equation 4x^2-8mx-9=0 has 1 root as the negative of the other

Question 222963: Find the value of 'm' such that the equation 4x^2-8mx-9=0 has 1 root as the negative of the other
Answer by jsmallt9(3758) (Show Source): 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.
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