Question

Questão 3: Resolva as equações do 2° grau e determine suas raízes
A)
${5}^{2} x - 3x - 2 = 0$

B)
${x}^{2} - 8x + 12 = 0$

C)
${x}^{2} + 2x - 8 = 0$

D)
$- {x}^{2} + x + 12 = 0$

E)
$- {x}^{2} + 6x - 5 = 0$

F)
${6}^{2} x + x - 1 = 0$

G)
${3}^{2} x - 7x + 2 = 0$

H)
${ x}^{2} = x + 12$

I)
$2x = 15 - {x}^{2}$

J)
${x}^{2} - 5x + 6 = 0$

K)
${x}^{2} - 7x + 12 = 0$

L)
${x}^{2} + 3x - 28 = 0$

M)
${x}^{2} - 3 = 4x + 2$

N)
$(x + 3) {}^{2} = 1$

O)
${x}^{2} + 9x + 8 = 0$
É urgente e para amanhã eu preciso de ajuda !!!!
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Answer 1

Explicação passo-a-passo:

RESOLUÇÃO!!!

5x²-3x-2=0

A=5

B=-3

C=-2

∆=b²-4ac

∆=(-3)²-4*5*-2

∆=9+40

∆=49

-b±√∆/2a

3±√49/2*5

3±7/10

X¹=3+7/10=10/10=>1

X²=3-7/10=-4/10=-4/10(÷2)=>-2/5

_____________________________

X²-8x+12=0

A=1

B=-8

C=12

∆=b²-4ac

∆=(-8)²-4*1*12

∆=64-48

∆=16

-b±√∆/2a

8±√16/2*1

8±4/2

X¹=8+4/2=12/2=>6

X²=8-4/2=4/2=>2

_____________________________

X²+2x-8=0

A=1

B=2

C=-8

∆=b²-4ac

∆=2²-4*1*-8

∆=4+32

∆=36

-b±√∆/2a

-2±√36/2*1

-2±6/2

X¹=-2+6/2=4/2=>2

X²=-2-6/2=-8/2=>-4

_____________________________

-x²+x+12=0

A=-1

B=1

C=12

∆=b²-4ac

∆=(-1)²-4*1*12

∆=1-48

∆=-47

-b±√∆/2a

-1±√-47/2*-1

-1±√-47/-2

Não possui solução no campo dos números reais.

_____________________________

-x²+6x-5=0

A=-1

B=6

C=-5

∆=b²-4ac

∆=6²-4*-1*-5

∆=36-20

∆=16

-b±√∆/2a

-6±√16/2*-1

-6±4/-2

X¹=-6+4/-2=-2/-2=>1

X²=-6-4/-2=-10/-2=>5

_____________________________

6x²+x-1=0

A=6

B=1

C=-1

∆=b²-4ac

∆=1²-4*6*-1

∆=1+24

∆=25

-b±√∆/2a

-1±√25/2*6

-1±5/12

X¹=-1+5/12=4/12=4/12(÷2)=>2/6=2/6(÷2)=>1/3

X²=-1-5/12=-6/12=-6/12(÷2)=-3/6=-3/6(÷3)=>-1/2

_____________________________

3x²-7x+2=0

A=3

B=-7

C=2

∆=b²-4ac

∆=(-7)²-4*3*2

∆=49-24

∆=25

7±√25/2*3

7±5/6

X¹=7+5/6=12/6=>2

X²=7-5/6=2/6=2/6(÷2)=>1/3

_____________________________

X²=x+12

X²-x-12=0

A=1

B=-1

C=-12

∆=b²-4ac

∆=(-1)²-4*1*-12

∆=1+48

∆=49

-b±√∆/2a

1±√49/2*1

1±7/2

X¹=1+7/2=8/2=>4

X²=1-7/2=-6/2=>-3

_____________________________

2x=15-x²

X²+2x-15=0

A=1

B=2

C=-15

∆=b²-4ac

∆=2²-4*1*-15

∆=4+60

∆=64

-b±√∆/2a

-2±√64/2*1

-2±8/2

X¹=-2+8/2=6/2=>3

X²=-2-8/2=-10/2=>-5

_____________________________

X²-5x+6=0

A=1

B=-5

C=6

∆=b²-4ac

∆=(-5)²-4*1*6

∆=25-24

∆=1

-b±√∆/2a

5±√1/2*1

5±1/2

X¹=5+1/2=6/2=>3

X²=5-1/2=4/2=>2

_____________________________

X²-7x+12=0

A=1

B=-7

C=12

∆=b²-4ac

∆=(-7)²-4*1*12

∆=49-48

∆=1

-b±√∆/2a

7±√1/2*1

7±1/2

X¹=7+1/2=8/2=>4

X²=7-1/2=6/2=>3

_____________________________

X²+3x-28=0

A=1

B=3

C=-28

∆=b²-4ac

∆=3²-4*1*-28

∆=9+112

∆=121

-b±√∆/2a

-3±√121/2*1

-3±11/2

X¹=-3+11/2=8/2=>4

X²=-3-11/2=-14/2=>-7

_____________________________

X²-3=4x+2

X²-4x-3-2=0

X²-4x-5=0

A=1

B=-4

C=-5

∆=b²-4ac

∆=(-4)²-4*1*-5

∆=16+20

∆=36

-b±√∆/2a

4±√36/2*1

4±6/2

X¹=4+6/2=10/2=>5

X²=4-6/2=-2/2=>-1

_____________________________

(X+3)²=1

X²+2x*3+3²=1

X²+6x+9=1

X²+6x+9-1=0

X²+6x+8=0

A=1

B=6

C=8

∆=b²-4ac

∆=6²-4*1*8

∆=36-32

∆=4

-b±√∆/2a

-6±√4/2*1

-6±2/2

X¹=-6+2/2=-4/2=>-2

X²=-6-2/2=-8/2=>-4

_____________________________

X²+9x+8=0

A=1

B=9

C=8

∆=b²-4ac

∆=9²-4*1*8

∆=81-32

∆=49

-b±√∆/2a

-9±√49/2*1

-9±7/2

X¹=-9+7/2=-2/2=>-1

X²=-9-7/2=-16/2=>-8

Espero ter ajudado!