Determine os valores dos coeficientes a, b, e c nas seguintes equações:
a) 2² – + 6 = 0 a = _____, b = _____ c = _____.
b) ² + 6 + 9 = 0 a = _____, b = _____ c = _____.
c) 3 + 2² – 10 = 0 a = _____, b = _____ c = _____.
d) ² – = 0 a = _____, b = _____ c = _____.
e) 3² – 9 = 0 a = _____, b = _____ c = _____.
Respostas
Resposta:
A) a = 1 b = -10 c = 21
completa
{3, 7}
B) a = -1 b = 14 c = -49
completa
{-7, 7}
C) a = 1 b = -2 c = 5
completa
{-1, 3}
D) a = 1 b = 1 b = -12
completo
{-4, 3}
E) a = 1 b = 8 c = 0
incompleto
{-8, 0}
F) a = 1 b = 0 c = -81
incompleto
{-9, 9}
G) a = 3 b = -15 c = 0
incompleto
{0, 5}
H) a = 4 b = 0 c = -49
incompleto
{-7/4, 7/4}
I) a = 1 b = -2 c = 1
completo
{-1, 1}
J) a = 2 b = -1 c = -10
completo
{5/2, 2}
Explicação passo-a-passo:
Bhaskara: -b +- raiz de delta ______________ delta: b²-4.a.c 2.a
A) x² - 10x + 21 = 0 a = 1 b = -10 c = 21
delta: (-10)² - 4.1.21
delta: 100 - 84
delta: 16
- (-10) +- raiz de 16 = 4 x' = 10 + 4 14
_________________ _____ = __ = 7
2.1 2.1 2
x" = 10 - 4 6
____ = __ = 3
2.1 2
B) -x² + 14x - 49 = 0 a = -1 b = 14 c = -49
delta: 14² - 4.(-1).(-49)
delta: 196 - 196
delta: 0
- 14 +- 0 x' = -14 - 0 -14
______ _____ = ___ = 7
2.(-1) -2 -2
x" = -14 + 0 -14
_____ = ___ = 7
-2 -2
C) x² - 2x + 5 = 0 a = 1 b = -2 c = 5
delta: (-2)² - 4.1.5
delta: 4 - 20
delta: 16
- (-2) +- 4 x' = 2 + 4 6
_______ ____ = __ = 3
2.1 2 2
x" = 2 - 4 -2
____ = __ = -1
2 2
D) x² + x - 12 = 0 a = 1 b = 1 c = - 12
delta: 1² - 4.1.(-12)
delta: 1 + 48
delta: 49
- 1 +- 7 x' = -1 + 7 6 x" = -1 -7 -8
_____ ____ = __ = 3 ___ = __ = -4
2.1 2.1 2 2 2
E) x² + 8x = 0 a = 1 b = 8 c = 0
x (x + 8) = 0
x = 0
x + 8 = 0
x = - 8
F) x² - 81 = 0 a = 1 b = 0 c = - 81
x² = 81
x = raiz quadrada de 81
x = 9 e -9
G) 3x² -15x = 0 a = 3 b = -15 c = 0
x (3x - 15) = 0
x = 0
3x - 15 = 0
3x = 15
x = 15/3 = 5
H) 4x² - 49 = 0 a = 4 b = 0 c = -49
4x² = 49
x² = 49/4
x = raiz de 49/4
x = - 7/4 e +7/4
I) x² - 2x + 1 = 0 a = 1 b = -2 c = 1
delta: (-2)² - 4.1.1
delta: 4 - 4
delta: 0
- (-2) +- 0 x = 2
_______ __ = 1
2.1 2
J) 2x² - x - 10 = 0 a = 2 b = -1 c = -10
delta: (-1)² - 4.2.(-10)
delta: 1 + 80
delta: 81
- (-1) +- raiz de 81 = 9 x' = 1 + 9 10 5
_____________ ____ = __ = __
2.2 2.2 4 2
x" = 1 - 9 8
___ = __ = 2
2.2 4
Explicação passo-a-passo: