Question

Obtenha as raízes das equações:

A)x²-x-6=0

B)3x²-2x-1=0

C)y²-7y+6=0

D)16x²+8x+1=0

E)4x²-7x+3=0

F)7x²+28x+21=0

G)x²+4x+3=0

Me ajudem por favor

Answer 1

a)x²-x-6=0
∆= (-1)²-4(1)(-6)
∆=1+24
∆=25
x¹=-(-1)+√25/2
x¹=1+5/2=3

x²=-(-1)-√25/2
x²= 1-5/2=-2

b)3x²-2x-1=0
∆=(-2)²-4.3(-1)
∆=4+12
∆=16

x¹= -(-2)+√16/2.6
x¹=2+4/12
x¹=6/12 simplifica por 6
x¹=1/2

x²=- (-2)-√16/12
x²= 2-4/12=-2/12
x²=-1/6

c) y²-7y+6=0
∆=(-7)²-4.1.6
∆=49-24
∆=25

y¹=- (-7)+√25/2
y¹= 7+5/2
y¹= 6

y²=-(-7)-√25/2
y²=7-5/2
y²= 1

d)16x²+8x+1=0
∆=8²-4.16.1
∆=64-64
∆=0

x¹=x²
x= -8+√0/2.16
x=-8+0/32
x=-8/32 simplifica por 8
x=-1/4

e)4x²-7x+3=0
∆=(-7)²-4.4.3
∆=49-48
∆=1

x¹=-(-7)+√1/2.4
x¹=7+1/8
x¹=8/8
x¹=1

x²=-(-7)-√1/2.4
x²=7-1/8
x²=6/8
x²=3/4

f)7x²+28x+21=0
∆=28²-4.7.21
∆=784-588
∆=196

x¹=-28+√196/2.7
x¹= -28+14/14
x¹=-14/14
x¹=-1

x²=-28-√196/2.7
x²=-28-14/14
x²=42/14
x²=3

g)x²+4x+3=0
∆=4²-4.1.3
∆=16-12
∆=4

x¹= -4+√4/2
x¹=-4+2/2
x¹=-2/2
x¹=-1

x²=-4-√4/2
x²=-4-2/2
x²=-6/2
x²=-3