Final answer:
The two numbers whose difference is 192 and whose product is a minimum are -96 and 96, because they are equidistant from zero on the number line.
Step-by-step explanation:
The question is asking to find two numbers whose difference is 192 and whose product is a minimum. To solve this, we can translate it into an optimization problem and use calculus or recognize it as a problem involving integers and their properties. However, the provided information and constants such as a, b, and c are irrelevant for this specific question.
Instead, we can employ a different strategy by observing that when the product of two numbers is minimized with a fixed difference, the numbers are equidistant from each other on the number line. In this case, the two numbers that are equidistant from zero (and therefore have the minimum product) with a difference of 192 will be -96 and +96.
The correct answer is option a): -96, 96.
To further illustrate, consider two numbers x and x + 192 with a product P = x(x + 192). The derivative of P with respect to x will show that the product is minimized when x = -96, confirming our pair of numbers.