What is the root of - x^2+12x-32

x = 4, x = 8

Step-by-step explanation:

To find the roots equate to zero, that is

- x² + 12x - 32 = 0 (multiply through by - 1)

x² - 12x + 32 = 0

Consider the factors of the constant term ( + 32) which sum to give the coefficient of the x - term ( - 12)

The factors are - 4 and - 8, since

- 4 * - 8 = + 32 and - 4 - 8 = - 12, thus

(x - 4) (x - 8) = 0

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 8 = 0 ⇒ x = 8