Question

Determine as raízes das equações {responda as que você sabe fazer)

x²+5x+6=0

x²-3x+2=0

x²-8x+15=0

x²-23x+120=0

x²+3x-4=0

3x²+4x+1=0

5x²+13-6=0

7x²-17x-12=0

12x²+x-6=0

25x-25x+6=0

4x²+20x+25=0

Answer 1

Eaew!!!



Resolução!!!



1) x² + 5x + 6 = 0


a = 1
b = 5
c = 6


∆ = 5² - 4.1.6
∆ = 25 - 24
∆ = 1


x = -5 ± √1/2.1

x = -5 ± 1/2

x' = -5 - 1/2 = -6/2 = -3

x" = -5 + 1/2 = -4/2 = -2


S={ -3, -2}


===============================

2) x² - 3x + 2 = 0


∆ = (-3)² - 4.1.2
∆ = 9 - 8
∆ = 1


x = -(-3) ± √1/2.1

x = 3 ± 1/2

x' = 3 + 1/2 = 4/2 = 2

x" = 3 - 1/2 = 2/2 = 1


S={ 2, 1 }


===============================

3) x² - 8x + 15 = 0


∆ = (-8)² - 4.1.15
∆ = 64 - 60
∆ = 4


x = -(-8) ± √4/2.1

x = 8 ± 2/2

x' = 8 + 2/2 = 10/2 = 5

x" = 8 - 2/2 = 6/2 = 3


S={ 5, 3 }



===============================

4) x² - 23x + 120 = 0


∆ = (-23)² - 4.1.120
∆ = 529 - 480
∆ = 49


x = -(-23) ± √49/2.1

x = 23 ± 7/2

x' = 23 + 7/2 = 30/2 = 15

x" = 23 - 7/2 = 16/2 = 8


S={ 15, 8 }


===============================

5) x² + 3x - 4 = 0


∆ = 3² - 4.1.(-4)
∆ = 9 + 16
∆ = 25


x = -3 ± √25/2.1

x = -3 ± 5/2

x' = -3 + 5/2 = 2/2 = 1

x' = -3 - 5/2 = -8/2 = -4


S={ 1, -4 }


================================

6) 3x² + 4x + 1 = 0


∆ = 4² - 4.3.1
∆ = 16 - 12
∆ = 4


x = -4 ± √4/2.3

x = -4 ± 2/6

x' = -4 + 2/6 = -2/6 = -1/3

x" = -4 - 2/6 = -6/6 = -1


S={ -1/3, -1 }


===============================

7) 5x² + 13x - 6 = 0


∆ = 13² - 4.5.(-6)
∆ = 169 + 120
∆ = 289


x = -13 ± √289/2.5

x = -13 ± 17/10

x' = -13 + 17/10 = 4/10 = 2/5

x" = -13 - 17/10 = -30/10 = -3


S={ 2/5, -3 }



================================

8) 7x² - 17x - 12 = 0


∆ = (-17)² - 4.7.(-12)
∆ = 289 + 336
∆ = 625


x = -(-17) ± √625/2.7


x = 17 ± 25/14

x' = 17 - 25/14 = -8/14 = -4/7

x" = 17 + 25/14 = 42/14 = 3


S={ -4/7, 3 }


===============================


9) 12x² + x - 6 = 0


∆ = 1² - 4.12.(-6)
∆ = 1 + 288
∆ = 289


x = -1 ± √289/2.12

x = -1 ± 17/24

x' = -1 - 17/24 = -18/24 = -3/4

x" = -1 + 17/24 = 16/24 = 2/3


S={ -3/4, 2/3 }


==============================

10) 25x² - 25x + 6 = 0


∆ = (-25)² - 4.25.6
∆ = 625 - 600
∆ = 25


x = -(-25) ± √25/2.25

x = 25 ± 5/50

x' = 25 + 5/50 = 30/50 = 3/5

x" = 25 - 5/50 = 20/50 = 2/5


S={ 3/5, 2/5 }


===============================

11) 4x² + 20x + 25 = 0


∆ = 20² - 4.4.25
∆ = 400 - 400
∆ = 0


x = -20 ± 0/2.4

x = -20/8 = -5/2


S={ -5/2 }



★Espero ter ajudado!! tmj.