What Two Numbers Difference Is 12 And Product Is A Minimum?

Let the product be given by the function p(x) where the smallest number is x.
p(x) = x(x+12) = x² + 12x

P(x) defines a parabola, which will have a minimum at x=-12/2 = -6

The two numbers are -6 and +6.
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The minimum of the expression
ax² + bx + c
is at the value of x given by
x = -b/(2a)