Question

Usando a fórmula de bhaskara, resolva as seguintes equações do 2 grau

a) x2-4x+3=0

b)x2+2x-3=0

c) x2-7x-8=0

d) x2-81=0

Answer 1

a) x²-4x+3 = 0
a =1 b=-4 c=3
Δ = b² - 4.a.c
Δ = (-4)²-4.1.3
Δ = 16 - 12
Δ = 4
x = -b±√Δ / 2a ⇒ -(-4) ± √4 / 2 ⇒ 4±2 / 2
x1⇒4-2 = 4 / 2 = 2
x2⇒ 4+2 = 6 / 2 =4

b) x²+2x-3 = 0
a =1 b= 2 c = -3
Δ=b²-4.a.c
Δ=2²-4.1.(-3)
Δ=4+12 
Δ=16
x=-b±√Δ / 2.a ⇒ -2±√16 / 2 ⇒ -2±4 / 2
x1=-2+4 = 2 / 2 = 1 
x2=-2-4 = -4 / 2 = -2

c) x²-7x-8 = 0
a= 1 b=-7 c=-8
Δ=b²-4.a.c
Δ=(-7)²-4.1.(-8)
Δ=49+32
Δ=81
x=-b±√Δ / 2.a ⇒ -(-7)±√81 / 2 ⇒7±9 / 2
x1= 7-9 = -2 / 2 = -1
x2=7+9 = 16 / 2 = 8

d)x²-81 = 0
a=1 b=0 c=-81
Δ=b²-4.a.c
Δ=0²-4.1.(-81)
Δ=324
x=-b±√Δ / 2.a ⇒ 0±√324 / 2 ⇒ 0 ± 18 / 2 
x1=0-18 = -18 / 2 = -9
x2=0+18 = 18 / 2 = 9