Question

Determine os zeros das funções:

a) f(x) = - 6x² + 2x + 4

b) f(x) = 4x² - 24x + 36

Answer 1

a)

- 6x² + 2x + 4 = 0

x² - x/3 = 2/3

x² - x/3 + 1/36 = 2/3 + 1/36

(x - 1/6)² = 25/36

(x - 1/6)² = 5²/6²

x - 1/6 = ± 5/6

x = 1/6 ± 5/6

x1 = 1/6 + 5/6

x1 = 6/6

x1 = 1

x2 = 1/6 - 5/6

x2 = - 4/6

b)

4x² - 24x + 36 = 0

x² - 6x = - 9

x² - 6x + 9 = - 9 + 9

(x - 3)² = 0

x - 3 = 0

x = 3

x1 = x2 = 3

Resposta:

a) x = 1 e x = - 4/6

b) x = 3 e x = 3