Respostas

2014-05-21T12:49:19-03:00
A) x² - 7x + 6 = 0
Δ = (-7)^2-4.1.6
Δ = 49-24
Δ = 25

X = \frac{-(-7)+- \sqrt{25} }{2.1} => X= \frac{7+-5}{2}

x' =  \frac{7+5}{2} =  \frac{12}{2} = 6                     x" =  \frac{7-5}{2} =  \frac{2}{2}  = 1

S = {6, 1}

b) - x² + 12x - 20 = 0
Δ = 12^2-4.(-1).(-20)
Δ = 144-80
Δ = 64

X= \frac{-12+- \sqrt{64} }{2.(-1)} => X = \frac{-12+-8}{-2}

x' =  \frac{-12+8}{-2} =  \frac{-4}{-2} = 2                      x" =  \frac{-12-8}{-2}= \frac{-20}{-2} =10

S = {2, 10}

c) x² + 5x + 6 = 0
Δ = 5^2-4.1.6
Δ = 25-24
Δ = 1

X =  \frac{-5+- \sqrt{1} }{2.1} => X= \frac{-5+-1}{2}

x' =  \frac{-5+1}{2}= \frac{-4}{2} =-2                   x" =  \frac{-5-1}{2}= \frac{-6}{2}=-3

S = {- 2, - 3}

d) 4x² + 4x + 1 = 0
Δ = 4^2-4.4.1
Δ = 16-16
Δ = 0

X =  \frac{-4+-  \sqrt{0} }{2.4} => X =  \frac{-4}{8} ou 0,5

S = {- 4/8 ou 0,5}

e) x² - 2x + 15 = 0
Δ = (-2)^2-4.1.15
Δ = 4-60
Δ = -56

Não possui raízes.

;D