4) Ache as raizes das funções abaixo, por Bhaskara:
a) y = x2 - 8x + 15
c) y = x2 + 6x + 8
e) y = x2 - 5x + 6
b) y = 2x2 + 7x + 5
d) y = x² + 12x +11
Soluções para a tarefa
Resposta:Segue as contas baixo na explicação
Explicação passo-a-passo:
a)x² - 8x + 15=0 b)2x² + 7x + 5=0 c)x² + 6x + 8=0
Δ=b²-4.a.c Δ=b²-4.a.c Δ=b²-4.a.c
Δ=(-8)²-4.1.15 Δ=7²-4.2.5 Δ=6²-4.1.8
Δ=64-60 Δ=49-40 Δ=36-32
Δ=4 Δ=9 Δ=4
x=-b ±√Δ/2.a x=-b ±√Δ/2.a x=-b ±√Δ/2.a
x=-(-8) ±√4/2.1 x=-7 ±√9/2.2 x=-6 ±√4/2.1
x=8 ± 2/2 x=-7 ± 3/4 x=-6 ± 2/2
x1=8+2/2 x1=-7+3/4 x1=-6+2/2
x1=10/2 x1=-4/4 x1=-4/2
x1=5 x1=-1 x1=-2
x2=8-2/2 x2=-7-3/4 x2=-6-2/2
x2=6/2 x2=-10/4:2/2 x2=-8/2
x2=3 x2=-5/2 x2=-4
S(5,3) S(-1,-5/2) S(-2,-4)
d)x² + 12x +11=0 e) x² - 5x + 6=0
Δ=b²-4.a.c Δ=b²-4.a.c
Δ=12²-4.1.11 Δ=(-5)²-4.1.6
Δ=144-44 Δ=25-24
Δ=100 Δ=1
x=-b ±√Δ/2.a x=-b ±√Δ/2.a
x=-12 ±√100/2.1 x=-(-5) ±√1/2.1
x=-12 ± 10/2 x=5 ± 1/2
x1=-12+10/2 x1=5+1/2
x1=-2/2 x1=6/2
x1=-1 x1=3
x2=-12-10/2 x2=5-1/2
x2=-22/2 x2=4/2
x2=-11 x2=2
S(-1,-11) S(3,2)
Resposta:
Explicação passo-a-passo:
A) x^2 -8x + 15 = 0
X = -b +- √b^2-4.a.c
2.a
X = -(-8) +- √8^2 - 4.1.15
2.1
X = 8 +- √64 -60
2
X = 8+- 2. 8+2/2 = 5 e 8-2/2 = 3
2
B) 2x^2 + 7x + 5
X = - 7 +- √49 - 40
4
X = -7 +- 3 -7 + 3/4 = -1
4 -7 - 3/4 = -2,5
C)x^2 + 6x + 8
X = -6 +- √36-32
2
X = - 6 +- 2 -6 +2/2 = -2
2 -6 - 2/2 = -4
D)x^2 + 12x + 11
X = - 12 +- √144 - 44
2
X = -12 +- 10 -12 +10 = -1
2 2
-12 - 10 = -11
2
E) x^2 - 5x + 6
X = -(-5) +-√25 -24
2
X = 5 +- 1 = 5-1 = 2 5+1 = 3
2 2 2