Two positive numbers differ by 4 and their product is 96.
(a) If the smaller number is taken to be x, set up a quadratic equation in x using the given conditions.
(b) Solve the quadratic equation and write down both obtained values of x.
(c) Identify the two required numbers, giving a clear reason for discarding any inadmissible value.
(d) Check your answer by showing that the product of the numbers you have chosen is indeed 96.