Question

Por meio da formula de baskara,resolva cada equação

a) x2 - 6x + 5 =0
b)3x2 + 4x + 1 =0
c) x2 - 8x + 16= 0
d) x2 - 13x + 22 = 0
e) -x2 + 10x - 25 = 0
f)7x2 - 1x - 1 =0
g) x2 -11x +10 = 0
h) 6x2 - x - 2 = 0
i) x2 - 2x + 1 = 0​

Answer 1

a)x²-6x+5=0

a=1, b=-6, c=5

∆=b²-4ac

∆=(-6)²-4.1.5

∆=36-25

∆=11

x=-b±√∆/2a

x=6±√11/2.1

x=6±√11/2

x1=6+√11/2

x2=6-√11/2

S={6+√11/2, 6-√11/2}

b)3x²+4x+1=0

a=3, b=4, c=1

∆=b²-4ac

∆=4²-4.3.1

∆=16-12

∆=4

x=-b±√∆/2a

x=-4±√4/2.3

x=-4±√4/6

x1=-4+√4/6

x2=-4-√4/6

S={-4+√4/6, -4-√4/6}

c)x²-8x+16=0

a=1, b=-8, c=16

∆=b²-4ac

∆=(-8)²-4.1.16

∆=64-64

∆=0

x=-b±√∆/2a

x=8±√0/2.1

x=8±0/2

x=8/2=4

S={4}

d)x²-13x+22=0

a=1, b=-13, c=22

∆=b²-4ac

∆=(-13)²-4.1.22

∆=169-88

∆=81

x=-b±√∆/2a

x=13±√81/2.1

x=13±9/2

x1=13+9/2=22/2=11

x2=13-9/2=4/2=2

S={11,2}

e)-x²+10x-25=0

a=-1, b=10 c=-25

∆=b²-4ac

∆=10²-4.(-1).(-25)

∆=100-100

∆=0

x=-b±√∆/2a

x=-10±√0/2.(-1)

x=-10±0/-2

x=-10/-2

x=-5

S={-5}

f)7x²-1x-1=0

a=7, b=-1 c=-1

∆=b²-4ac

∆=(-1)²-4.7.(-1)

∆=1+28

∆=29

x=-b±√∆/2a

x=1±√29/2.7

x=1±√29/14

x1=1+√29/14

x2=1-√29/14

S={1+√29/14, 1-√29/14}

g)x²-11x+10=0

a=1, b=-11, c=10

∆=b²-4ac

∆=(-11)²-4.1.10

∆=121-40

∆=81

x=-b±√∆/2a

x=11±√81/2.1

x=11±9/2

x1=11+9/2=20/2=10

x2=11-9/2=2/2=1

S={10,1}

h)6x²-x-2=0

a=6, b=-1 c=-2

∆=b²-4ac

∆=(-1)²-4.6.(-2)

∆=1+48

∆=49

x=-b±√∆/2a

x=1±√49/2.6

x=1±7/12

x1=1+7/12=8/12=4/6=2/3

x2=1-7/12=-6/12=-3/6=-1/3

S={-1/3, 2/3}

i)x²-2x+1=0

a=1, b=-2, c=1

∆=b²-4ac

∆=(-2)²-4.1.1

∆=4-4

∆=0

x=-x±√∆/2a

x=2±√0/2.1

x=2±0/2

x=2/2

x=1

S={1}