Jawab:

Penjelasan dengan langkah-langkah:

suku banyak

akar akar  

jumlah dan  hasil kali

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soal

2x³ - x² - 18x + p=  0, akar akar x₁ , x₂ dan x₃

a= 2 , b = -1 , c = -18, d = p

x₁ + x₂ +x₃ = -b/a = 1/2

x₁  x₂ + x₁ x₃ + x₂ x₃ = c/a= -18/2 = -9

x₁ . x₂ . x₃ = -d/a = -p/2

sepasang saling berlawanan, misal

x₁ =  - x₂ ⇒ x₁ + x₂ =  0

i) x₁ + x₂ +x₃ = 1/2

(x₁ + x₂) +x₃ = 1/2

0 + x₃ = 1/2

x₃ = 1/2

ii) x₁  x₂ + x₁ x₃ + x₂ x₃ = -9

x₁  x₂ + (x₁+ x₂ ) x₃ = -9

x₁  x₂ + (0) (1/2) = -9

x₁  x₂ = - 9

iii) x₁ . x₂ . x₃ = -p/2

(-9)(1/2) = -p/2

-9/2 = -p/2

p= 9

iv) hasil kali  = x₁ . x₂ .x₃ = (-9)(1/2) = -9/2