SOLUTION: What is the greatest possible product that can be formed by two integers whose sum is -256? Show how u figured it out.

Question 432888: What is the greatest possible product that can be formed by two integers whose sum is -256? Show how u figured it out.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
p(x) = x*(-256 - x) = -x^2 - 256x
That's a parabola that opens down, so the vertex is a max.
The line of symmetry is x = -b/2a = 256/-2
x = -128
p(-128) = -16384 - 256*(-128)
= 16384
--------
The 2 integers are -128 & -128
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Another approach:
-256/2 = -128
Product of any 2 integers that add to -256 =
(-128 + x)*(-128 - x) where x = any integer from 0 to 128
Product = 16384 - x^2
For the product to be a max, x^2 has to be a minimum. Minimum = 0
--> -128 * -128

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