Jawab:

Penjelasan dengan langkah-langkah:

Menentukan akar persamaan kuadrat dengan menggunakan cara memfaktorkan

a. 3x² - 12 = 0

3x² - 12 = 0

3 (x² - 4) = 0

3 (x² - 2²) = 0 [selisih kuadrat a² - b² = (a +b) (a - b)]

3 (x + 2) (x - 2) = 0

x + 2 = 0

x₁ = -2

atau

x - 2 = 0

x₂ = 2

HP = {-2, 2}

b. x² + 7x + 6 = 0

p × q = 6 = 1 × 6

p + q = 7 = 1 + 6

x² + 7x + 6 = 0

(x + 6) (x + 1) = 0

x + 6 = 0

x₁ = -6

atau

x + 1 = 0

x₂ = -1

HP = {-6, -1}

c. -3x² - 5x + 2 = 0

-3x² - 5x + 2 = 0 kesemua dikali negatif

3x² + 5x - 2 = 0

a × c = 3 × -2 = -6

p × q = -6 = 6 × -1

p + q = 5 = 6 + -1

3x² + 5x - 2 = 0

3x² + 6x - 1x - 2 = 0

3x (x + 2) - 1(x + 2) = 0

(3x - 1) (x + 2) = 0

3x - 1 = 0

3x = 1

x₁ = 1/3

atau

x + 2 = 0

x₂ = -2

HP = {-2, 1/3}