Question

Resolva as equações de 2 grau usando a formula de Bhaskara. (Com cálculos)

a) X² - 7x = 0
b) X² - 5x = 0
c) 4x² - 9x = 0
d) 3x² + 5x = 0
e) 4x² - 12x = 0​

Answer 1

Explicação passo-a-passo:

a) x² - 7x = 0

a= 1; b = -7; c = 0

D = (-7)² - 4 . 1 . 0

D = 49 - 0

D = 49

x = (-b +- VD)/2a

x = ( - (-7) +/- V49)/2 . 1

x = (7 +/- 7)/2

x' = (7 + 7)/(2)

x' = (14)/(2)

x' = 7

x'' = (7 - 7)/( 2)

x'' = (0)/( 2)

x'' = 0

S = {(0, 7)}

b) x² - 5x = 0

a= 1; b = -5; c = 0

D = (-5)² - 4 . 1 . 0

D = 25 - 0

D = 25

x = (-b +- VD)/2a

x = ( - (-5) +/- V25)/2 . 1

x = (5 +/- 5)/2

x' = (5 + 5)/(2)

x' = (10)/(2)

x' = 5

x'' = (5 - 5)/( 2)

x'' = (0)/( 2)

x'' = 0

S = {(0, 5)}

c) 4x² - 9x = 0

a= 4; b = -9; c = 0

D = (-9)² - 4 . 4 . 0

D = 81 - 0

D = 81

x = (-b +- VD)/2a

x = ( - (-9) +/- V81)/2 . 4

x = (9 +/- 9)/8

x' = (9 + 9)/(8)

x' = (18)/(8)

x' = 9/4

x'' = (9 - 9)/( 8)

x'' = (0)/( 8)

x'' = 0

S = {(0, 9/4)}

d) 3x² + 5x = 0

a= 3; b = 5; c = 0

D = 5² - 4 . 3 . 0

D = 25 - 0

D = 25

x = (-b +- VD)/2a

x = ( - 5 +/- V25)/2 . 3

x = (-5 +/- 5)/6

x' = (-5 + 5)/(6)

x' = (0)/(6)

x' = 0

x'' = (-5 - 5)/( 6)

x'' = (-10)/( 6)

x'' = -5/3

S = {(-5/3, 0)}

e) 4x² - 12x = 0

a= 4; b = -12; c = 0

D = (-12)² - 4 . 4 . 0

D = 144 - 0

D = 144

x = (-b +- VD)/2a

x = ( - (-12) +/- V144)/2 . 4

x = (12 +/- 12)/8

x' = (12 + 12)/(8)

x' = (24)/(8)

x' = 3

x'' = (12 - 12)/( 8)

x'' = (0)/( 8)

x'' = 0

S = {(0, 3)}