Question

Resolva as equações: 1) x² - 5x + 6 = 0 (R: 2, 3) 2) x² - 8x + 12 = 0 (R: 2, 6)
3) x² + 2x - 8 = 0 (R: 2, -4)
4) x² - 5x + 8 = 0 (R: vazio)
5) 2x² - 8x + 8 = 0 (R: 2,)
6) x² - 4x - 5 = 0 (R: -1, 5)
7) -x² + x + 12 = 0 (R: -3, 4)
8) -x² + 6x - 5 = 0 (R: 1, 5)
9) 6x² + x - 1 = 0 (R: 1/3 , -1/2)
10) 3x² - 7x + 2 = 0 (R: 2, 1/3)
11) 2x² - 7x = 15 (R: 5, -3/2)
12) 4x² + 9 = 12x (R: 3/2)
13) 4x² - x + 1 = x + 3x² (R: 1)
14) 3x² + 5x = -x – 9 + 2x² (R: -3)
15) 4 + x ( x - 4) = x (R: 1,4)
16) x ( x + 3) – 40 = 0 (R: 5, -8)
17) (x + 3)² = 1 (R:-2,-4)
18) (x - 5)² = 1 (R:3,7)
19) (2x - 4)² = 0 (R:2)
20) (x - 3)² = -2x² (R:vazio)​

Answer 1

1) x² - 5x + 6 = 0

∆= b²-4ac

∆= 25 -4.1.6

∆= 25-24

∆= 1

x'= -b+√∆/2.a

x'= 5+1/2.1

x'= 6/2

x'= 3

x"= -b-√∆/2a

x"= 5-1/2

x"= 2

2) x² - 8x + 12 = 0

∆= b²-4ac

∆= 64-4.1.12

∆= 64-48

∆= 16

x'= -b+√∆/2a

x'= 8+4/2

x'= 6

x"= -b-√∆/2a

x"= 8-4/2

x"= 2

3) x² + 2x - 8 = 0

∆= b²-4ac

∆= 4-4.1.-8

∆= 36

x'= -b+√∆/2a

x'= 2+6/2

x'= 4

x"= -b-√∆/2a

x"= 2-6/2

x"= -2

4) x² - 5x + 8 = 0 (R: vazio)

∆= b²-4ac

∆= 25-4.1.8

∆= 25-32

∆>0 Não pertence aos reais.

5) 2x² - 8x + 8 = 0 (÷2)

x²-4x-4=0

∆= b²-4ac

∆= 4 - 4.1.-4

∆= 4+16

∆= 20

x'= -b+√∆/2a

x'= 4 +2√5/2

x'= 2+1√5

x"= -b-√∆/2a

x"= 4 -2√5/2

x"= 2-1√5

6) x² - 4x - 5 = 0

∆= b²-4ac

∆= 16 -4.1.-5

∆= 36

x'= -b+√∆/2a

x'= 4 + 6/2

x'= 5

x"= -b-√∆/2a

x"= 4-6/2

x"= -2/2 = -1

7) -x² + x + 12 = 0 (R: -3, 4)

∆= b²-4ac

∆= 1 -4.(-1).12

∆= 48 +1

∆= 49

x'= -b+√∆/2a

x'= -1+7/-2

x'= -3

x"= -b-√∆/2a

x"= -1-7/-2

x"= +4

8) -x² + 6x - 5 = 0

∆= b²-4ac

∆= 36 -4.(-1).-5

∆= 36 -20

∆= 16

x'= -b+√∆/2a

x'= -6 + 4 / -2

x'= 1

x"= -b-√∆/2a

x"= -6-4/-2

x"= 5

9) 6x² + x - 1 = 0

∆= b²-4ac

∆= 1 - 24.(-1)

∆= 25

x'= -b+√∆/2a

x'= -1 +5/12 = 4/12 = 2/6 = 1/3

x"= -b-√∆/2a

x"= -1-5/12 = -1/2

10) 3x² - 7x + 2 = 0

∆= b²-4ac

∆= 49 -4.3.2

∆= 49-24 = 25

x'= -b+√∆/2a

x'= 7+5/6

x'= 12/6= 2

x"= -b-√∆/2a

x"= 7-5/6

x"= 2/6 = 1/3

11) 2x² - 7x = 15

2x²-7x-15=0

∆= b²-4ac

∆= 49-4.2.-15

∆= 49+120

∆ = 169

x'= -b+√∆/2a

x'= 7+13/2.2

x'= 20/4

x'= 5

x"= -b-√∆/2a

x"= 7 -13 / 4

x"= -6/4

x"= -3/2

12) 4x² + 9 = 12x

4x²-12x-9= 0

∆= b²-4ac

∆= 144-4.4.-9

∆= 144-144

x'= -b+√∆/2a

x'= 12 + 0/8

x'= 6/4 = 3/2

x"= -b-√∆/2a

x"= 12+0/8= 3/2

13) 4x² - x + 1 = x + 3x²

4x²-3x²-x-x+1= 0

x²-2x+1=0

∆= b²-4ac

∆= 4-4.1.1

∆= 0

x'= -b+√∆/2a

x'= 2+0/2

x'= 1

x"= -b-√∆/2a

x"= 2-0/2

x"= 1

14) 3x² + 5x = -x – 9 + 2x²

3x²5x+x+9-2x²= 0

x²+6x+9= 0

∆= b²-4ac

∆= 36 - 36

∆= 0

x'= -b+√∆/2a

x'= -6+0/2

x'= -3

x"= -b-√∆/2a

x"= -6-0/2

x"= -3

15) 4 + x ( x - 4) = x

4+x²-4x-x= 0

x²-5x+4= 0

∆= b²-4ac

∆= 25 -4.1.4

∆= 9

x'= -b+√∆/2a

x'= 5 +3/2

x'= 8/2

x'= 4

x"= -b-√∆/2a

x"= 5-3/2

x"= 1

16) x ( x + 3) – 40 = 0

x²+3x-40=0

∆= b²-4ac

∆= 9 - 4.1.(-40)

∆= 169

x'= -b+√∆/2a

x'= -3+13/2

x'= 10/2

x'= 5

x"= -b-√∆/2a

x"= -3-13/2

x"= -16/2 = -8

17) (x + 3)² = 1

x²+6x+9-1= 0

x²+6x-8= 0

∆= b²-4ac

∆= 36 - 32

∆= 4

x'= -b+√∆/2a

x'= -6+2/2

x'= -4/2 = -2

x"= -b-√∆/2a

x"= -6 -2/2

x"= -8/2 = -4

18) (x - 5)² = 1

(x-5).(x-5)-1= 0

x²-10x+24=0

∆= b²-4ac

∆= 100-4.1.24

∆= 100-96 = 4

x'= -b+√∆/2a

x'= 10+2/2

x'= 6

x"= -b-√∆/2a

x"= 10-2/2

x"= 4

19) (2x - 4)² = 0

(2x-4).(2x-4)=0 (÷2)

(x-2).(x-2)= 0

x²-4x+4= 0

∆= b²-4ac

∆= 16 -4.1.4

∆= 16- 16

∆= 0

x'= -b+√∆/2a

x'= -4+0/2

x'= -2

x"= -b-√∆/2a

x"= -4+0/2

x"= -2

20) (x - 3)² = -2x²

(x-3).(x-3) +2x²=0

x²-6x+9+2x²= 0

3x²-6x+9= 0 (÷3)

x²-2x+3= 0

∆= b²-4ac

∆= 4 -1.1.3

∆= 4-12

∆= -8

∆<0 não pertence aos reais. Resultado conjunto vazio