Solve the problem.
-What is the minimum product of two numbers whose difference is 84?
A) -3528
B) -21
C) -42
D) -1764

Question

Quizplus · Accepted Answer

Let x and y be the two numbers. We know that x - y = 84. Rearranging this equation, we get x = y + 84. The product of x and y is (y + 84) * y = y^2 + 84y. This is a quadratic function that opens upwards, meaning it has a minimum value at its vertex. The x-coordinate of the vertex is -b/2a, where a is the coefficient of the y^2 term and b is the coefficient of the y term. In this case, a = 1 and b = 84. So the x-coordinate of the vertex is -84/2 = -42. Plugging this x-coordinate back into the quadratic function, we get the minimum product as (-42)^2 + 84*(-42) = -1764. Therefore, the answer is D, -1764.

Solve the Problem. -What Is the Minimum Product of Two Numbers Whose Difference