Question

5) Resolva as seguintes equações: a) 5x² + 100x - 320 = 0. b) x² + 12x + 36 = 0. c) 3x² - 75 = 0. d) 6x² + 18x = 0.​

Answer 1

a) 5x² + 100x - 320 = 0

(-b±$\sqrt{b²-4.a.c})$/2.a

(-(100)±$\sqrt{100²-4.5.(-320)})$/2.5

(-100±$\sqrt{10000-20.(-320)})$/10

(-100±$\sqrt{10000-6400})$/10

(-100±$\sqrt{3600})$/10

(-100±60)/10

x1=-160/10=-16

x2=-40/10=-4

b) x² + 12x + 36 = 0

(-b±$\sqrt{b²-4.a.c})$/2.a

(-12±$\sqrt{12²-4.1.36})$/2.1

(-12±$\sqrt{144-144})$/2

(-12±$\sqrt{0})$/2

-12±1/2

x1=-13/2 = -6,5

x2=-11/2 = -5,5

c) 3x² - 75 = 0

(-b±$\sqrt{b²-4.a.c})$/2.a

(0±$\sqrt{-4.3.(-75)})$/2.3

(0±$\sqrt{900})$/6

0±30/6

x1=30/6=5

x2=-30/6=-5

d) 6x² + 18x = 0

(-b±$\sqrt{b²-4.a.c})$/2.a

(-18±$\sqrt{18²-4.6.0})$/2.6

(-18±$\sqrt{324})$/12

-18±18/12

x1=0/12 = 0

x2=-36/12 = -3