Question

me ajudem, equações do 2°grau​

Answer 1

Resposta:

Explicação passo-a-passo:

a)

Δ= b²- 4ac

Δ= 13² - 4.1.36

Δ= 169 - 144

Δ= 25

x= -b +- √Δ / 2.a

x= - 13 +- √25 / 2.1

x= -13 +- 5 / 2

x = -13 +5 / 2

x = -8 / 2  

x = -4

 

x = - 13 - 5 / 2

x = -18 / 2

x = - 9

S[-4, -9]

_______________

b)

a=1 b=-2 c=7

∆=b²-4ac

∆=(-2)²-4•1•7

∆= -12

S = {∅}

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c)

x² - 6x + 5 = 0

Δ = b² - 4.a.c

Δ = (-6)² - 4.(1).(+5)

Δ = 36 - 20

Δ = 16

x= - b ± √Δ/2.a

       

x = - (-6) ± √16/2.1

           

x = + 6 ± 4/2

          

x' = 6 + 4/2 =  10/2   =  5

        

x"= 6 - 4/2  = 2/2 = 1

     

S = [1, 5]

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d)

Δ= b² - 4.a.c

Δ = 10² - 4.1.25

Δ = 100 - 100

Δ = 0  

Se Δ=0 temos que x1 = x2

x = - b +-√Δ /2a

         

x = -10 +- √0/2.1 = -10/2 = -5

                 

x = 5

S = [5]

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e)

x² -6x +9 =0

Δ= b²-4ac

Δ= (-6)² -4.1.9

Δ=36 -36

Δ=0

x= -b +/- √Δ / 2a

x= -(-6) +/- √0 / 2.1

x'= 6 / 2

x'= 3

x''=3

S = [3]

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f)

x²-2x+1=0  

a= 1 b= -2 c= 1  

Δ=b²-4ac  

Δ=(-2)²-4·1·1  

Δ= 4 -4  

Δ=0  

x= -b +/-√Δ/2a  

x= 2 +/-0/2·1  

x'= 2/2=1  

x''= 2/2= 1  

S = [1]

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g)

4x²+8x+3=0

Δ= b²-4ac 

Δ = 8² -(4*4*3)  = 64-48 = 16

x=-b+\-√Δ/2a  

x =  -8+\-√16/2*4

x = -8+\-4/8

                     

x'=- -8+4/8  =  -4/8   = -1/2 ou 0,5

x"=- -8-4/8  = -12/8   = -1/1,5 ou 1,5

   

s{-1/2 ou 0,5 ; -1 .1/2 ou 1,5}

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h)

x²+x+4=0  

Δ=b² - 4.a.c

Δ= 1² -4. 1. 4

Δ=1-16

Δ= -15

S = {∅}

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i)

x²-6x+5=0

Δ = b² -4 .a .c

Δ = (-6)² - 4. 1 .5

Δ = 36  -20

Δ = 16

x = -b +- √Δ / 2.a

x = - (-6)  + - √16/2 . 1

x = 6 +- 4/ 2

x' = 6 + 4/2

x' = 10/2

x' = 5

x" = 6 - 4/2

x" = 2/2

x" = 1

S{ 5 e 1 }

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j)

9x² + 6x + 4 = 0

Δ = b² - 4 . a .c

Δ = 6² - 4 . 9 . 4

Δ = 36 - 144

Δ = -108

S = {∅}

Bons Estudos!!!