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Soluções para a tarefa
Resposta:
a) x² - 6x + 7 = 0
a = 1
b = - 6
c= 7
∆= b² - 4ac
∆= (-6)² - 4×1×7
∆= 36 - 28
∆= 64
√∆= 8
x= -b +- √∆ /2a
x= -(-6) +-8/2×1
x1= 6+8/2= 14/2= 7
x2= 6-8/2= -2/2= -1
S= {7,-1}
b) x² + 3x - 28 = 0
a= 1
b= 3
c= -28
∆= b² - 4ac
∆= 3²- 4×1×(-28)
∆= 9 + 112
∆= 121
√∆= 11
x= -b +-√∆/2a
x= -3 +-11/2×1
x1= -3+11/2= 8/2= 4
x2= -3-11/2= -14/2= -7
S= {4,-7}
c) 4x² - 12x + 7 = 0
a= 4
b= -12
c= 7
∆= b² - 4ac
∆= (-12)² -4×4×7
∆= 144 - 112
∆= 32
√∆= 4√2
x= -b +-√∆/2a
x= -(-12) +-4√2/2×4
x1= 12+4√2/8= 16√2/8= 2√2
x2= 12-4√2/8= 8√2/8= √2
S= {2√2,√2}
d) x² + 8x + 16 = 0
a= 1
b= 8
c= 16
∆= b² - 4ac
∆= 8² - 4×1×16
∆= 64 - 64
∆= 0
x= -b +-√∆/2a
x= -8 +-0/2×1
x1= -8+0/2= -8/2= -4
x2= -8-0/2= -8/2= -4
S= {-4,-4}
e) 3x² - 2x + 1= 0
a= 3
b= -2
c= 1
∆= b² - 4ac
∆= (-2)² - 4×3×1
∆= 4 - 12
∆= -8
S= Não existi, pois não existi raíz quadrada de um número negativo!!
f) x² - 5x = 0
a= 1
b= -5
c= 0
∆= b² - 4ac
∆= (-5)² - 4×1×0
∆= 25- 0
∆= 25
√∆= 5
x= -b +-√∆/2a
x= -(-5) +-5/2×1
x1= 5+5/2= 10/2= 5
x2= 5-5/2= 0/2= 0
S= {5,0}
g) x² - 25 = 0
a= 1
b= 0
c= -25
∆= b² - 4ac
∆= 0²- 4×1×(-25)
∆= 0 + 100
∆= 100
√∆= 10
x= -b +-√∆/2a
x= 0 +-10/2×1
x1= 0+10/2= 10/2= 5
x2= 0-10/2= -10/2= -5
S= {5,-5}
h)2x² - 100 = 0
a= 2
b= 0
c= -100
∆= b² - 4ac
∆= 0² - 4×2×(-100)
∆= 0 + 800
∆= 800
√∆= 20√2
x= -b +-√∆/2a
x= -0 +-20√2/2×2
x1= 0+20√2/4= 20√2/4= 5√2
x2= 0-20√2/4= -20√2/4= -5√2
S= {5√2,-5√2}