Question

Determine o conjunto verdade de cada uma das equações de 2.° grau, sendo U = IR:

a) x² - 4x + 3 = 0

b) 2x² - 10x + 12 = 0

c) x² - 5x - 14 = 0

Answer 1

A)

x² —4x + 3 = 0

∆ = (—4)²—4*1*3

∆ = 16 —12

∆ = 4

x1 = ( 4+2)/2*1

x1 = 6/2 = 3

x1 = 3

x2 = (4—2)/2*1

x2 = 2/2 = 2

x2 = 2

Sol : { 2 ; 3 }

C)

2x²—10x+12 = 0

∆ = (—10)²—4*2*12

∆ = 100 — 96

∆ = 4

x1 = (10+2)/2*2

x1 = 12/4 = 3

x2 = (10—2)/2*2

x2 = 8/4 = 2

Sol: { 2 ; 3 }

C)

x²—5x—14 = 0

∆ = (—5)²—4*1*(—14)

∆ = 25 +56

∆ = 81

x1 = ( 5+9)/2*1

x1 = 14/2 = 7

x2 = (5—9)/2*1

x2 = —4/2 = —2

Sol: {—2 ; 7 }

Dúvidas??Comente!!

Answer 2

Resposta:

A)

x² —4x + 3 = 0

∆ = (—4)²—4*1*3

∆ = 16 —12

∆ = 4

x1 = ( 4+2)/2*1

x1 = 6/2 = 3

x1 = 3

x2 = (4—2)/2*1

x2 = 2/2 = 2

x2 = 2

Sol : { 2 ; 3 }

C)

2x²—10x+12 = 0

∆ = (—10)²—4*2*12

∆ = 100 — 96

∆ = 4

x1 = (10+2)/2*2

x1 = 12/4 = 3

x2 = (10—2)/2*2

x2 = 8/4 = 2

Sol: { 2 ; 3 }

C)

x²—5x—14 = 0

∆ = (—5)²—4*1*(—14)

∆ = 25 +56

∆ = 81

x1 = ( 5+9)/2*1

x1 = 14/2 = 7

x2 = (5—9)/2*1

x2 = —4/2 = —2

Sol: {—2 ; 7 }

ESPERO TER LHE AJUDADO