Question

Determine as raízes das equações:
a) x2 - x - 20 = 0
b) x2 - 3x -4 = 0
c) x2 - 8x + 7 = 0

Answer 1

Resposta:

a) x² - x - 20 = 0

Δ = (-1)² - 4 . 1 . -20

Δ = 1 + 80

Δ = 81

$x = \frac{- (-1) + \sqrt{81}}{2}$

$x = \frac{1 + 9}{2}$

$x = \frac{10}{2}$

x = 5

$x = \frac{- (-1) - \sqrt{81}}{2}$

$x = \frac{1 - 9}{2}$

$x = \frac{-8}{2}$

x = -4

b) x² - 3x - 4 = 0

Δ = (-3)² - 4 . 1 . -4

Δ = 9 + 16

Δ = 25

$x = \frac{- (-3) + \sqrt{25}}{2}$

$x = \frac{3 + 5}{2}$

$x = \frac{8}{2}$

x = 4

$x = \frac{- (-3) - \sqrt{25}}{2}$

$x = \frac{3 - 5}{2}$

$x = \frac{-2}{2}$

x = -1

c) x² - 8x + 7 = 0

Δ = (-8)² - 4 . 1 . 7

Δ = 64 - 28

Δ = 36

$x = \frac{- (-8) + \sqrt{36}}{2}$

$x = \frac{8 + 6}{2}$

$x = \frac{14}{2}$

x = 7

$x = \frac{- (-8) - \sqrt{36}}{2}$

$x = \frac{8 - 6}{2}$

$x = \frac{2}{2}$

x = 1