Question

calcule as raízes das equações de segundo grau:

a) f(x) = x² - 4x + 3

b) f(x) = x² - 9x + 20

c) f(x) = -2x² - x

d) f(x) = -3x² + 18

Answer 1

a: x=1 x=3
b: x=4 x=5

Answer 2

a) x²-4x+3
∆= (-4)² - 4•1•3
∆ = 16- 12
∆= 4
x= -(-4) ± √4
2•1
x= 4 ± 2
2
x= 4+2 = 6 = 3
2 2
x= 4-2 = 2 = 1
2. 2
S= {3,1}

b) x²-9x+20
∆= (-9)² - 4•1•20
∆= 81-80
∆= 1
x = -(-9) ±√1
2
x= 9 ± 1
2
x= 9+1 = 10 = 5
2 2
x= 9-1 = 8 = 4
2 2
S= {5,4}

c) - 2x² - x (-1)
2x² + x
x (2x + 1)
x = o
2x = 1
x= 1
2
S= {0, 1}
2
d)-3x + 18
-3x²= -18 (-1)
3x²= 18
x²= 18 = x² = 6
3
x= ± √6
x= ± 3
S= {3,-3}