Question

Calcule as raizes das equações : a) 9y^ - 24y + 16= 0
b)-x^ + 11 x - 28 = 0
c) x^ + 5 x = 6
d) 6x^ + 5x 1 = 0
e) x^ - 2 x = 0
f) x^ - 49 = 0
g) 4x^ = 0
h) 2x^ + x = 0
Dou 15 pts !!!

Answer 1

a)
9y²-24y+16 = 0
Δ = b²-4.a.c
Δ = (-24)²-4.9.16
Δ = 576 -576
Δ = 0
y = -b ± √Δ/2.a
y = -(-24) ± √0/2.9
y = 24 ± 0/18
y = 24/18
y = 4/3


b)
-x² + 11x - 28= 0
Δ = b²-4.a.c
Δ = 11²-4.(-1).(-28)
Δ = 121-112
Δ = 9
x = -b ± √Δ/2a
x = -11 ± √9/2.(-1)
x = -11 ± 3/-2
x' = -11+3/-2
x' = -8/-2
x' = 4
x" = -11-3/-2
x" = -14/-2
x" = 7


c)
x²+5x-6 = 0
Δ = b²-4.a.c
Δ = 5²-4.1.(-6)
Δ = 25 + 24
Δ = 49
x = -b ± √Δ/2a
x = -5 ± √49/2.1
x = -5 ± 7/2
x ' = -5+7/2
x' = 2/2
x' = 1
x" = -5-7/2
x" = -12/2
x" = -6

d)
6x²+ 5x + 1= 0
Δ = b² -4.a.c
Δ = 5² - 4.6.1
Δ = 25-24
Δ = 1
x = -b ± √Δ/2a
x = -5 ± √1/2.6
x = -5 ± 1/12
x' = -5+1/12
x' = -4/12
x" = -5-1/12
x" = -6/12


e)
x²-2x = 0
Δ = b²-4.a.c
Δ = (-2)² -4.1.0
Δ = 4
x = -b ± √Δ/2a
x = -(-2) ± √4/2
x = 2 ± 2/2
x' = 2+2/2
x ' = 4/2
x' = 2
x" = 2-2/2
x" = 0/2
x" = 0


f)
x²-49= 0
Δ = b²-4.a.c
Δ = 0²-4.1.(-49)
Δ = 0 + 196
Δ = 196
x = -b ± √Δ/2a
x = 0 ± √196/2.1
x = 0 ± 14/2
x' = 0+ 14/2
x' = 14/2
x' = 7
x " = 0-14/2
x" = -14/2
x" = -7


g)
4x² = 0
Δ = b²-4.a.c
Δ = 0² - 4.4.0
Δ = 0
x -b ± √Δ/2a
x = 0 ± √0/2.4
x = 0 ± 0/8
x' e x" = 0


h)
2x²+ x = 0
Δ = b²-4.a.c
Δ = 1²-4.2.0
Δ = 1-0
Δ = 1
x = -b ± √Δ/2a
x = -1 ± √1/2.2
x = -1 ± 1/4
x' = -1+1/4
x' = 0/4
x' = 0
x" = -1-1/4
x" = -2/4