Question

Zapisz wielomian P(x)= - 21x +20 w postaci iloczynu trzech wielomianów stopnia pierwszego.

Answer 1

P(x) = x³ - 21x + 20 = x³ - x - 20x + 20 = x(x² - 1) - 20(x - 1) = x(x - 1)(x + 1) - 20(x - 1) = (x - 1) [x(x + 1) - 20] = (x - 1) (x² + x - 20)

 

x² + x - 20

Δ = 1 + 80 = 81

√Δ = 9

x1 = (-1 - 9)/2 = -10/2 = -5

x2 = (-1 + 9)/2 = 8/2 = 4

 

P(x) = (x - 1)(x + 5)(x - 4)  --- odpowiedz