Write the following as a quadratic equation. The product of two consecutive positive integers equals 56.
a) n (n + 1) = 56
b) n^2 = 56
c) n (n - 1) = 56
d) n (n + 2) = 56
The correct quadratic equation that represents the scenario where the product of two consecutive positive integers equals 56 is option A) n (n + 1) = 56.
To arrive at this solution, we need to understand what "consecutive positive integers" mean. Consecutive integers are numbers that follow each other in order without skipping any numbers. In this case, the two consecutive positive integers can be represented as 'n' and 'n + 1'.
Given that the product of these two consecutive positive integers equals 56, we can write the equation as: n (n + 1) = 56. This equation represents the multiplication of the two consecutive integers.
Option B) n^2 = 56 represents a square of a single integer, which is not accurate in this scenario. Option C) n (n - 1) = 56 represents the product of an integer and the integer that comes before it, which is not the case with consecutive positive integers. Option D) n (n + 2) = 56 represents the product of two integers that are two units apart, which does not satisfy the definition of consecutive positive integers.
Therefore, the correct answer is option A) n (n + 1) = 56.