Question

1) Determine as raízes ou zeros das seguintes funções quadráticas
a) f(x) = x² - 3x + 2
b) f(x) = 3x² - 7x + 2
c) f(x) = - 3x² + 6
d) f(x) = - 2x² + x
e) f(x) = 4x² + 3

Answer 1

Usando o complemento dos quadrados:

a)

x² - 3x + 2 = 0

x² - 3x = - 2

x² - 3x + 9/4 = - 2 + 9/4

(x - 3/2)² = 1/4

(x - 3/2)² = 1/2²

x - 3/2 = ± 1/2

x = (3 ± 1)/2

x1 = (3 + 1)/2

x1 = 4/2

x1 = 2

x2 = (3 - 1)/2

x2 = 2/2

x2 = 1

S = {1, 2}

b)

3x² - 7x + 2 = 0

x² - 7x/3 = - 2/3

x² - 7x/3 + 49/36 = -2/3 + 49/36

(x - 7/6)² = 25/36

(x - 7/6)² = 5²/6²

x - 7/6 = ± 5/6

x = (7 ± 5)/6

x1 = (7 + 5)/6

x1 = 12/6

x1 = 2

x2 = (7 - 5)/6

x2 = 2/6

x2 = 1/3

S = {2, 1/3}

c)

- 3x² + 6 = 0

- 3x² = - 6

3x² = 6

x² = 6/3

x² = 2

x = ± √2

S = {√2, -√2}

d)

- 2x² + x = 0

x(- 2x + 1) = 0

x = 0

ou

- 2x + 1 = 0

- 2x = - 1

2x = 1

x = 1/2

S = {0, 1/2}

e)

4x² + 3 = 0

4x² = - 3

x² = - 3/2²

x = ± √(- 3)/2

x = ± i√3/2

S = {i√3/2, - i√3/2}