Read the following information carefully and answer the questions given below. A set of natural numbers has to be formed that consists of six numbers,...

Read the following information carefully and answer the questions given below. A set of natural numbers has to be formed that consists of six numbers, and the last number is 30. The first number of the set is the highest root of the given equation, and the second number of the set is (n+4) - 2n, where ‘n’ is the difference between the roots of the given equation. The third number of the set is (n+1)²– (n+1). The fourth number of the set is (n+2)² – (n+2). The fifth number of the set is $(n+1)^3$ – (n+5). (Note: $x^2$ – 14x + 48 = 0)
Which of the following statements are correct?
I. The product of the second and fifth numbers is a perfect square.
II. The average of the last four numbers is 17.
III. If the seventh number is defined as the sixth number plus $n^3$, then this seventh number is a factor of 114.