Question

1) Verificando a fórmula de bhaskara resolva as equações de 2º grau:

a) x²+5x-14=0

b) x²-x-12=0

c) 2x²+2x-24=0

d) 2x²+x-1=0

e) 3x²-4x+1=0

Answer 1

x² + 5x - 14 = 0 

Delta = b² - 4ac
Delta = (5)² - 4(1)(-14)
Delta = 25 - 4(1)(-14)
Delta = 25 + 56
Delta = 81

X = (-b +- raiz delta) / 2a
X = (-b +- raiz delta) / 2(1)
X = (-5 +- 9) / 2
x' = (-5 + 9) / 2 = 4/2 = 2
x" = (-5 - 9) / 2 = -14/2 = -7

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b) x² - x - 12 = 0

Delta = b² - 4ac
Delta = (-1)² - 4(1)(-12)
Delta = 1 - 4(1)(-12)
Delta = 1 + 48
Delta = 49

X = (-b +- raiz delta) / 2a
X = (1 +- 7) / 2(1)
X = (1 +- 7) / 2
x' = (1 + 7) / 2 = 8/2 = 4
x" = (1 - 7) / 2 = -6/2 = -3

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c) 2x² + 2x - 24 = 0 

Delta = b² - 4ac
Delta = (2)² - 4(2)(-24)
Delta = 4 - 4(2)(-24)
Delta = 4 + 192
Delta = 196

X = (-b +- raiz delta) / 2a
X = (-2 +- 14) / 2(2)
X = (-2 +- 14) / 4
x' = (-2 + 14) / 4 = 12/4 = 3
x" = (-2 - 14) / 4 = -16/4 = -4

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

d) 2x² + x - 1 = 0

Delta = b² - 4ac
Delta = (1)² - 4(2)(-1)
Delta = 1 - 4(2)(-1)
Delta = 1 + 8
Delta = 9

X = (-b +- raiz delta) / 2a
X = (-1 +- 3) / 4
x' = (-1 + 3) / 4 = 2/4 = 1/2
x" = (-1 - 3) / 4 = -4/4 = -1

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e) 3x² - 4x + 1 = 0

Delta = b² - 4ac
Delta = (-4)² - 4(3)(1)
Delta = 16 - 4(3)(1)
Delta = 16 - 12
Delta = 4

X = (-b +- raiz delta) / 2a
X = (4 +- 2) / 6
x' = (4 + 2) / 6 = 6/6 = 1
x" = (4 - 2) / 6 = 2/6 = 1/3

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