Jawaban:

a.

pemfaktoran :

3x² - 12 = 0

3x² + 0x - 12 = 0

1x² + 0x - 4 = 0

(x + 2)(x - 2)

x1 :

x + 2 = 0

x = -2

x2 :

x - 2 = 0

x = 2

rumus kuadratik :

3x - 12 = 0

3x² + 0x - 12 = 0

a = 3 b = 0 c = -12

x1,2 = -b ± √b² - 4ac / 2a

= 0 ± √0 - 4(3)(-12) / 2(3)

= 0 ± √0 - (-144) / 6

= 0 ± √144 / 6

= 0 ± 12 /6

x1 :

0 + 12 / 6

= 2

x2 :

0 - 12 / 6

= -2

melengkapi kuadrat sempurna :

3x - 12 = 0

3x² + 0x - 12 = 0

1x² + 0x - 4 = 0

1x² + 0x = 4

1x² + 0x + (0/2)² = 4 + (0/2)²

1x² + 0x + 0² = 4 + 0²

(x + 0)² = 4 + 0

x + 0 = √4

x + 0 = ±2

x1 :

x = 2

x2 :

x = -2

b.

pemfaktoran :

x² + 7x + 6 = 0

(x + 6)(x + 1)

x1 :

x + 6 = 0

x = -6

x2 :

x + 1 = 0

x = -1

rumus kuadratik :

x² + 7x + 6 = 0

a = 1 b = 7 c = 6

x1,2 = -b ± √b² - 4ac / 2a

= -7 ± √7² - 4(1)(6) / 2(1)

= -7 ± √49 - 24 / 2

= -7 ± √25 / 2

= -7 ± 5 / 2

x1 :

-7 + 5 / 2

= -2 / 2

= -1

x2 :

-7 - 5 / 2

= -12 / 2

= -6

melengkapi kuadrat sempurna :

x² + 7x + 6 = 0

x² + 7x = - 6

x² + 7x + (7/2)² = -6 + (7/2)²

x² + 7x + (7/2)² = -6 + 49/4

(x + 7/2)² = -24/4 + 49/4

(x + 7/2)² = 25/4

x + 7/2 = √25/4

x + 7/2 = ±5/2

x1 :

x + 7/2 = 5/2

x = 5/2 - 7/2

x = -2/2

x = -1

x2 :

x + 7/2 = -5/2

x = -5/2 - 7/2

x = -12/2

x = -6

c.

x1 = -2

x2 = 1/3