Question

rozłóż na czynniki wielomain

w(x)=x^3-2x+1

Answer 1

x³ - 2x + 1 = x³ - x - x + 1 = x ( x² - 1) - ( x - 1) = x ( x - 1)( x + 1) - ( x - 1) = (x - 1 ) [ x(x + 1 ) - 1 ] =

( x - 1) (x² + x - 1 ) = ( x - 1 ) (x +1/2 + √5/2) ( x +1/2 - √5/2)

 

x² + x  - 1 =0

Δ = 1 + 4 = 5

x₁= ( -1 -√5) / 2 = -1/2 - √5/2

x₂ = ( -1 + √5) / 2 = -1/2 +√5/2