kunci matematika 1

1. Penyelesaian :
3x² - x – 2 = 0
(3x – 2) (x + 1) = 0
3x – 2 = 0 V x + 1 = 0
3x = 2 x = -1
X =
+ =
+ =

2. Penyelesaian :
(x – a)² =
X – a =
(2x – 3) (x – 1) =0
2x – 3 = 0 V x – 1 = 0
2x = 3 x – 1 = 0
X = x = -1
X = → x – 0 =
- a =
-a = -

-a = -
-a = -
a =

3. Penyelesaian :
6x² + x – 2 = 0 dan x₁ > x₂
Maka x₁ - x₂ = ...
(3x + 2) (2x – 1)
3x = -2, 2x = 1
X = , x = →
x₁ - x₂ = - = 1

4. Penyelesaian :
x₁ - x₂ =

=

=

=

= -24

5. Penyelesaian :
Petunjuk :
(x₁ = maka x₁x₂ =
x² =
1 =
C = a

6. Penyelesaian :
X + x² = 12
x² + x – 12 = 0
(x + 4) (x – 3) = 0
X + 4 = 0 V x – 3 = 0
X = -4 V x = 3
Dua kali bilangan positif = 2.3 =6

7. Penyelesaian :
X(x + 8) = 48
x² + 8x = 48
x² + 8x – 48 = 0
(x + 12) (x – 4) = 0
X + 12 = 0 V x – 4 = 0
X = -12 V x = 4
X = 4 → 3x = 3.4 = 12

8. Penyelesaian :
5(x – 1) = 3x² + 5
5x – 5 = 3x² + 5
3x² + 5 – 5x + 5 = 0
3x² - 5x + 10 = 0
D = b² - 4ac
= (-5)² - 4.3.10
= 25 – 120
= -95

9. Penyelesaian :
a. x² + 8x – 4 = 0
b² - 4ac = 8² - 4.1 (-4)
= 64 + 16
= 80
b. x² + 12x + 36 = 0
b² - 4ac = 12² - 4.1.36
= 144 - 144
= 0
c. x² + 3x + 4 = 0
b² - 4ac = 3² - 4.1.4
= 9 - 16
= -7

d. x² + 2x + 6 = 0
b² - 4ac = 2² - 4.1.6
= 4 - 24
= -20


10. Penyelesaian :
a. 3x² - 12x + 12 = 0
b² - 4ac = (-12)² - 4.3.12
= 144 - 144
= 0
b. 3x² + 12x – 12 = 0
b² - 4ac = 12² - 4.3.(-12)
= 144 + 144
= 288
c. -3x² - 12 + 12 = 0
b² - 4ac = (-12)² - 4.(-3).12
= 144 + 144
= 288
d. -3x² - 12x - 12 = 0
b² - 4ac = (-12)² - 4 (-3) (-12)
= 144 - 144
= 0

1. Penyelesaian :
-3x² + 4 – 1 > 0
→ -3x² + 4 – 1 > 0
-3x² + 3 > 0 =
(-3x – 3 ) (x – 1) < 0 -3x – 3 > V x – 1 < 0 -3x > 3 V x < 1 X > -1

2. Penyelesaian :
12 – 5x – 2x² < 0 → 2x² + 5x – 12 < 0 (-2x + 3) (x + 4) = 0 -2x + 3 = 0 V x + 4 = 0 -2x = -3 V x + 4 = 0 X = x = -4 X = 1 3. Penyelesaian : x² - 1 > 0
sehingga Hp = {x|x < - 1 atau x> 1, x € R}
x₂ - 1 = 0 V x² + 1 = 0
x² = 1 V x² = -1
x = 1 V x = -1

4. Penyelesaian :
x² + 6x + 10 > 0
definitif positif → x positif
semua bilangan yang digunakan baik positif maupun negatif hasilnya positif, maka {x|x € R}

5. Penyelesaian :
-4x² + 4x + 4 > 0
(-2x + 2)(2x + 2) > 0 → -4x² - 2x + 4x + 4

x₁ x₂











V

- < x < + 6. Penyelesaian : y = x² - 1 = x² - 1 - = 0 x² - (1 + )= → a = 1 → b = 0 → c = - (1 + ) Syarat real D ≥ 0 b² - 4ac ≥ 0 0² - 4-1. - (1 + ) ≥ o y = 1 → 0 4 + ≥ 0 → ≥ -4 ≤ y ≤ -1 y ≤ 1 atau y = 0 7. Penyelesaian : y = x² = xy – y x² - xy + y = 0 → a = 1 b = -y c = y D < 0 → bilangan kompleks (tidak real) b² - 4ac < 0 → (y)² - 4.1.y < 0 y² - 4y < 0 y(y-4) < 0 y = 0 V y = 4 0 < y < 4 8. Penyelesaian : K = 100 m² K = 2(p x ℓ) = 100 ℓ = 50 – p L = p .ℓ = p(50 - ℓ) < 600 50p - p² < 600 -p² + 50p – 600 < 0 9. Penyelesaian : Talang → p = 150 ℓ = 100 – 2x volume > 120.000 cm²
V = p.ℓ.t > 120.000
150 (100 – 2x) x > 120.000
15.000x – 300x² > 120.000 > 0
-x² + 50x – 400 < 0 10. Penyelesaian : ℓ = 1,5 > x

3 > 6x – 2x - x²
0 > 4x - x² - 3
0 > - x² + 4x – 3

x² 4x + 3 < 0