Jawab:

Penjelasan dengan langkah-langkah:

suku banyak

jumlah danhasil kali  akar akr

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soal

x³ + 6x² = a - 14x

x³ + 6x² + 14x -a = 0, akar x₁, x₂, dan x₃

a= 1 ,  b = 6 , c = 14 ,  d= - 1

i)  x₁= x₂ + x₃

ii)  x₁+ (x₂+x₃) = -b/a = - (6)/1 = - 6

x₁ +  x₁ = -6

2x₁ = - 6

x₁ = -3

x₁ = x₂+x₃

x² + x³ = - 3

iii)  x₁x₂+ x₁x₃+ x₂x₃ = c/a = -14/1 = -14

(x₁x₂+ x₁x₃)+ x₂x₃ = -14

x₁ (x₂+x₃)  +  x₂x₃ = -14

-3(-3)  + x₂x₃ = - 14

9 + x₂x₃ = - 14

x₂x₃ = -14 - 9

x₂x₃ = - 23

iv)  x₁ x₂ x₃ = -d/a =  a/1= a

-3(-23) = a

a=  69