Question

1) determinar as raízes das equações a seguir, utilizando a fórmula resolutiva: a) x²- x - 20=0 b)x²-3x-4=0 c)x² - 8x + 7=0.

Answer 1

Resposta:

a) x' = - 4 e x'' = 5

b) x' = - 1 e x'' = 4

c) x' = 1 e x'' = 7

Explicação passo a passo:

a) x²- x - 20=0

x = (-b ± √(b² - 4 • a • c)) / (2 • a)

x = (-(-1) ± √((-1)² - 4 • 1 • (-20))) / (2 • 1)

x = (1 ± √(1 - 4 • (-20))) / 2

x = (1 ± √(1 + 80)) / 2

x = (1 ± √81) / 2

x = (1 ± √9²) / 2

x = (1 ± 9) / 2

x' = (1 - 9) / 2

x' = - 8 / 2

x' = - 4

x'' = (1 + 9) / 2

x'' = 10 / 2

x'' = 5

b)x²-3x-4=0

x = (-b ± √(b² - 4 • a • c)) / (2 • a)

x = (-(-3) ± √((-3)² - 4 • 1 • (-4))) / (2 • 1)

x = (3 ± √(9 - 4 • (-4))) / 2

x = (3 ± √(9 + 16)) / 2

x = (3 ± √25) / 2

x = (3 ± √5²) / 2

x = (3 ± 5) / 2

x' = (3 - 5) / 2

x' = - 2 / 2

x' = - 1

x'' = (3 + 5) / 2

x'' = 8 / 2

x'' = 4

c)x² - 8x + 7=0

x = (-b ± √(b² - 4 • a • c)) / (2 • a)

x = (-(-8) ± √((-8)² - 4 • 1 • 7)) / (2 • 1)

x = (8 ± √(64 - 28)) / 2

x = (8 ± √36) / 2

x = (8 ± √6²) / 2

x = (8 ± 6) / 2

x = 4 ± 3

x' = 4 - 3

x' = 1

x'' = 4 + 3

x'' = 7