Question

Resolva as equações do 2 grau
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) x2 = x + 12 (R: -3 , 4)
14) 2x2 = -12x - 18 (R: -3)
15) x2 + 9 = 4x
(R: vazio)
16) 25x2 = 20x -4 (R: 2/5)
17) 2x = 15 x2 (R: 3,-5)
18) x2 + 3x - 6 = -8 (R: -1,-2).
19) x2 + x-7= 5 (R: -4,3)
20) 4x2 - x + 1 = x + 3x2 (R: 1)
21) 3x2 + 5x = -x - 9+ 2x2 (R: -3).

Answer 1

1) x2 - 5x + 6=0

a=1 ∆=b²-4.a.c x=-b+-√∆/2a

B=-5 ∆=25-4.1.6 x=5 + - √1/2

c=6 ∆=25-24 x=5+ - 1/2

∆= 1 x1=5+1/2

x1=6/2 x1= 3

x2=5-1/2

x2=4/2 x2=2

2)

${x}^{2} - 8x + 12 = 0$

a=1 ∆= b²-4.a.c x=-b + - √∆/2a

B= -8 ∆= 64-48 x=8+-√16/2.1

c=12 ∆= 16 x= 8+-4/2

x1=8+4/2 x1=12/2

x1= 6

x2=8-4/2 x2=4/2=2

3)

${ x}^{2} + 2x - 8 = 0$

a=1 ∆=b² -4.a.c x= -b +-√∆/2a

B=2 ∆= 4+32 x=-2+-√36/2.1

c=-8 ∆=36 x=-2+-6/2

x1=-2+6/2 x1=4/2

x1=2

x2=-2-6/2 x2=-8/2

x2=-4

4)

${x}^{2} - 5x + 8 = 0$

a=1 ∆=b²-4a.c R)não existe raiz de

B=-5 ∆=25-64 número negativo.

c=8 ∆= -39

5)

$2 {x}^{2} - 8x + 8 = 0$

a=2 ∆=b² -4.a.c x=-b + -√∆/2a

B=-8 ∆=64 -64 x=8+-√0/2.2

c=8 ∆=0 x=8/4 x=2

6)

${x}^{2} - 4x - 5 = 0$

a=1 ∆=b² - 4.a.c x=-b + - √∆/2a

B=-4 ∆=16+20 x=4+-√36/2.1

c=-5 ∆=36 x=4-+6/2

x1=4+6/2 x1=10/2

x1=5

x2=4-6/2 x2=-2/2

x2=-1

7)

$- {x}^{2} + x + 12 = 0$

a=-1 ∆=b² - 4.a.c x=-b + - √∆/2a

B=1 ∆=1+48 x=-1+-√49/2.1

c=12 ∆=49 x=-1+-7/2

x1=-1+7/2 x1=6/2=3

x2=-1-7/2

x2=-8/2 x2=-4

8)

$- {x}^{2} + 6x - 5 = 0$

a=-1 ∆=b² - 4.a.c x=-b + - √∆/2a

B=6 ∆=36-20 x=-6+-√16/2.(-1)

c=-5 ∆=16 x=-6+-4/-2

x1=-6+4/-2

x1=-2/-2 x1=-1

x2=-2-4/-2

x2=-6/-2 x=3

9)

$6 {x}^{2} + x - 1 = 0$

a=6 ∆=b² - 4.a.c x=-b + - √∆/2a

B=1 ∆=1+24 x=-1+-√25/2a

c=-1 ∆=25 x=-1+-5/12

x1=-1+5/12 x1=4/12

x1=1/3

x2=-1-5/12 x2=-6/12

x2=-1/2

10)

$3 {x}^{2} - 7x + 2 = 0$

a=3 ∆=b² - 4.a.c x=-b + - √∆/2a

B=-7 ∆=49-24 x=7-+√25/2.3

c=2 ∆=25 x=7+-5/6

x1=7+5/6 x1=12/6

x1=2

x2=7-5/6 x2=2/6

x2=1/3

11)

$2 {x}^{2} - 7x - 15 = 0$

a=2 ∆=b² - 4.a.c x=-b + - √∆/2a

B=-7 ∆=49+120 x=7+-√169/2.2

c=-15 ∆=169 x=7+-13/4

x1=7+13/4 x1=20/4

x1=5

x2=7-13/4 x2=-6/4

x2=-3/2

12)

$4 {x}^{2} - 12x + 9 = 0$

a=4 ∆=b² - 4.a.c x=-b + - √∆/2a

B=-12 ∆=144-144 x=12+-√0/2.4

c=9 ∆=0 x=12/8 x=3/2

13)

${x}^{2} - x - 12 = 0$

a=1 ∆=b² - 4.a.c x=-b + - √∆/2a

B=-1 ∆=1+48 x=1+-√49/2.1

c=-12 ∆=49 x=1+-7/2

x1=1+7/2 x1=8/2

x1=4

x2=1-7/2 x2=-6/2

x2=-3

14)

$2 {x}^{2} + 12 + 18 = 0$

a=2 ∆=b² - 4.a.c x=-b + - √∆/2a

B=12 ∆=144-144 x=-12+-√0/2.2

c=18 ∆=0 x=-12/4 x=-3

15)

${x}^{2} - 4x + 9 = 0$

a=-4 ∆=b² - 4.a.c não possuí raiz

B=9 ∆=18+16 real

c=0 ∆=34

16)

$25 {x}^{2} - 20x + 4 = 0$

a=25 ∆=b² - 4.a.c x=-b + - √∆/2a

B=-20 ∆=400-400 x=20+-√0/2.25

c=4 ∆=0 x=20/50 x=2/5

17)

$- {x}^{2} + 2x - 15 = 0$

a=-1 ∆=b² - 4.a.c não existe raiz de

B=2 ∆=4-60 número negativo.

c=-15 ∆=-56

18)

${x}^{2} + 3x + 2 = 0$a=1 ∆=b² - 4.a.c não existe raiz de

B=3 ∆=6-8 número negativo.

c=2 ∆=-2

19)

${x}^{2} + x - 12 = 0$

a= 1 ∆=b² - 4.a.c não existe raiz de

B= 1 ∆=1-48 número negativo.

c=12 ∆=-47

20)

${x}^{2} - 2x + 1 = 0$

a=1 ∆=b2 - 4.a.c x=-b + - √∆/2a

B=-2 ∆=4-4 x=2+-√0/2.1

c=1 ∆=0 x=2/2 x=1

21)

${x}^{2} + 6x + 9 = 0$

a=1 ∆=b2 - 4.a.c x=-b + - √∆/2a

B=6 ∆=36-36 x=-6+-√0/2.1

c=9 ∆=0 x=-6/2 x=-3

Espero ter ajudado ;-)