The lowest possible product would be -5625 given the numbers 75 and -75.
We can find this by setting the first number as x + 150, which we see in the equation given above. The other number would have to be simply x since it has to have a 150 difference.
Next we'll multiply the numbers together.
x(x+150)
x^2 + 150x
Now we want to minimize this as much as possible, so we'll find the vertex of this quadratic graph. You can do this by finding the x value as -b/2a, where b is the number attached to x and a is the number attached to x^2
-b/2a = -150/2(1) = -150/2 = -75
So we know one of the values is -75. We can plug that into the equation to find the second.
x + 150
-75 + 150
75
