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)
Soluções para a tarefa
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