jika (x-1) dan (x-2) adalah faktor-faktor dari f (x) = x^3+ax^2-bx+8 dan x1

Polinomial
Kelas XI

f(x) = x³ + ax² - bx + 8

(x - 1) faktornya , berarti f(1) = 0

f(1) = 1 + a - b + 8
0 = a - b + 9
-9 = a - b ... (i)

(x - 2) faktornya , berarti f(2) = 0

f(2) = 2³ + 2²a - 2b + 8
0 = 16 + 4a - 2b
-16 = 4a - 2b [÷ 2]
-8 = 2a - b ... (ii)

Eliminasi (i) dan (ii)

a - b = -9
2a - b = -8
––––––– (–)
-a = -1
a = 1

1 - b = -9
b = 1 + 9
b = 10

Maka f(x) = x³ + x² - 10x + 8
f(x) = (x - 1)(x - 2)(x + a)

Cari a :
a = 8 ÷ (-2) ÷ (-1)
a = 4

f(x) = (x - 1)(x - 2)(x + 4)

Dengan x₁ < x₂ < x₃ , Didapat x₁ = -4 , x₂ = 1 , x₃ = 2

Maka -x₁ + x₂ + x₃ = -(-4) + 1 + 2 = 7

smoga membantush_!

#jwbnny ad dipict, nocopas