Answer:
n = - 2, n = 8
Step-by-step explanation:
To obtain the roots equate f(n) to zero, that is
n² - 6n - 16 = 0
To factor consider the quadratic
Consider the factors of the constant term (- 16) which sum to give the coefficient 0f the n- term (- 6)
The factors are - 8 and + 2, since
- 8 × 2 = - 16 and - 8 + 2 = - 6, hence
(n - 8)(n + 2) = 0
Equate each factor to zero and solve for n
n - 8 = 0 ⇒ n = 8
n + 2 = 0 ⇒ n = - 2
