Factor. Find the roots. Show your work.

f (n) = n^2 - 6n - 16

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