Question

PRA HOJE RAPAZIADA AJUDA AQUI KKJ


Resolva as equações de 2o grau utilizando a fórmula de Bhaskara.
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)

Answer 1

Resposta:

1) (R: 2, 3)

2) (R: 2, 6)

3) (R: 2, -4)

4) (R: vazio)

5) (R: 2,)

6) (R: -1, 5)

7) (R: -3, 4)

8) (R: 1, 5)

9) (R: 1/3 , -1/2)

10) (R: 2, 1/3)

Explicação passo-a-passo:

1) x² - 5x + 6 = 0

a=1 b= -5 c=6

∆= b² -4.a.c

∆= (-5)² -4.1.6

∆= 25 - 24

∆= 1

x= -b ± √∆ / 2.a

x= -(-5) ± √1 / 2.1

x= 5 ±1 /2

x'= 5+1 /2 —> x'= 6/2 —> x'= 3

x"= 5-1 /2 —> x"= 4/2 —> x"= 2

2) x² - 8x + 12 = 0

a=1 b= -8 c=12

∆= (-8)² -4.1.12

∆= 64 - 48

∆= 16

x= -(-8) ±√16 /2.1

x= 8 ±4 /2

x'= 8+4 /2 —> x'= 12/2 —> x'= 6

x"= 8-4 /2 —> x"= 4/2 —> x"= 2

3) x² + 2x - 8 = 0

a=1 b=2 c= -8

∆= 2² -4.1.(-8)

∆= 4+32

∆=36

x= -2 ±√36 /2.1

x= -2 ±6 /2

x'= -2+6 /2 —> x'= 4/2 —> x'= 2

x"= -2-6 /2 —> x"= -8/2 —>x"= -4

4) x² - 5x + 8 = 0

a=1 b= -5 c=8

∆= (-5)² -4.1.8

∆= 25 - 32

∆= -7

x= -(-5) ±√-7 /2.1

x= 5 ±√-7 /2 —> Não existe raíz quadrada de número negativo

5) 2x² - 8x + 8 = 0

a=2 b= -8 c=8

∆= (-8)² -4.2.8

∆= 64 - 64

∆= 0

x= -(-8) ±√0 /2.2

x= 8±0 /4

x'= 8+0 /4 —> x'= 8/4 —> x'= 2

x"= 8-0 /4 —> x"= 8/4 —> x"= 2

6) x² - 4x - 5 = 0

a=1 b= -4 c= -5

∆= (-4)² -4.1.(-5)

∆= 16 + 20

∆= 36

x= -(-4) ±√36 /2.1

x= 4 ±6 /2

x'= 4+6 /2 —> x'= 10/2 —> x'=5

x"= 4-6 /2 —> x"= -2/2 —> x"= -1

7) -x² + x + 12 = 0

a= -1 b=1 c=12

∆= 1² -4.(-1).12

∆= 1 + 48

∆= 49

x= -1 ±√49 /2.(-1)

x= -1 ±7 /-2

x'= -1+7 /-2 —> x'= 6/-2 —> x'= -3

x"= -1-7 /-2 —> x"= -8/-2 —> x"= 4

8) -x² + 6x - 5 = 0

a= -1 b=6 c= -5

∆= 6² -4.(-1).(-5)

∆= 36 - 20

∆= 16

x= -6 ±√16 /2.(-1)

x= -6 ±4 /-2

x'= -6+4 /-2 —> x'= -2/-2 —> x'= 1

x"= -6-4 /-2 —> x"= -10/-2 —> x"= 5

9) 6x² + x - 1 = 0

a=6 b=1 c= -1

∆= 1² -4.6.(-1)

∆= 1 + 24

∆= 25

x= -1 ±√25 /2.6

x= -1±5 /12

x'= -1+5 /12 —> x'= 4/12 (÷4) —> x'= ⅓

x"= -1-5 /12 —> x"= -6/12 (÷6) —> x"= -½

10) 3x² - 7x + 2 = 0

a=3 b= -7 c=2

∆= (-7)² -4.3.2

∆= 49 - 24

∆= 25

x= -(-7) ±√25 /2.3

x= 7 ±5 /6

x'= 7+5 /6 —> x'= 12/6 (÷6) —> x'= 2/1 —> x'= 2

x"= 7-5 /6 —> x"= 2/6 (÷2) —> x"= ⅓