EQUAÇÃO DE 2° GRAU:
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
Soluções para a tarefa
Explicação passo-a-passo:
1) x² - x -20=0
∆= (-1)² -4.1.(-20)
∆= 1 + 80
∆= 81
x = - (-1) ±√81/2.1
x= 1 ±9/2
x1= 1+9/2= 10/2= 5
x2= 1-9/2= -8/2= -4
S = { -4, 5}
2) x² -7x +12=0
∆= (-7)² -4.1.12
∆= 49 - 48
∆= 1
x= - (-7) ±√1/2.1
x= 7 ±1/2
x1= 7+1/2= 8/2=4
x2= 7-1/2= 6/2=3
S= { 3, 4}
3) 3y² +2y - 1=0
∆= 2² - 4.3.(-1)
∆= 4 + 12
∆= 16
y= - 2 ±√16/2.3
y= - 2 ±4/6
y1= -2+4/6= 2/6= 1/3
y2= -2 -4/6= -6/6= -1
S= { -1, 1/3}
4) x² +6x +9=0
∆= 6² - 4.1.9
∆= 36 - 36
∆= 0
x= - 6±√0/2.1
x= -6/2
x= -3
S = { - 3}
5) 9x² -6x +9=0
∆= (-6)² -4.9.9
∆= 36 - 324
∆= - 288
Não existe raiz quadrada de número negativo
S = { } vazio
6) se for:
- 3t²+1t +4=0
3t² - t - 4=0
∆= (-1)² - 4.3.(-4)
∆= 1 + 48
∆= 49
t = - (-1) ±√49/2.3
t= 1 ±7/6
t1= 1+7/6= 8/6= 4/3
t2= 1-7/6= -6/6= -1
S = { - 1, 4/3}
7) x² - 2x -1=0
∆= (-2)² -4.1.(-1)
∆= 4 + 4
∆= 8
x = - (-2) ±√8/2.1
x= 2 ± √8/2
*8= 2.2.2= 2².2
√8= √2².2= 2√2
x= 2 ±2√2/2
x1= 1 + √2
x2= 1 - √2
S = { 1+√2 , 1-√2}
8) 6y² +y -1=0
∆= 1² - 4.6 .(-1)
∆= 1 + 24
∆= 25
y= - 1 ±√25/2.6
y= - 1 ±5/12
y1= -1+5/12= 4/12= 1/3
y2= -1-5/12= -6/12= - 1/6
S = { -1/6, 1/3}
9) u² +4u -5=0
∆= 4² -4.1.(-5)
∆= 16 + 20
∆= 36
u= - 4 ±√36/2.1
u= -4 ±6/2
u1= -4 +6/2= 2/2=2
u2= -4-6/2= -10/2= -5
S = { -5, 2}
10)-16x² +8x-1=0
16x² -8x +1= 0
∆= (-8)² - 4.16.1
∆= 64 - 64
∆= 0
x = -(-8)/2.16
x= +8/32
x= 1/4
S = { 1/4}