Question

Rozwiąż równanie: a) x^3 - 2x^2 + 2 =x b)x^3 + 5x^2 + 3x + 15 = 0

Answer 1

 a) x³ - 2x² + 2 =x

x³ - 2x²  -x +2= 0

x²(x-2) -1(x-2)=0

(x-2)(x²-1)=0

(x-2)(x-1)(x+1)=0

x=2 ∨ x=1 ∨ x=-1

b)x³ + 5x² + 3x + 15 = 0

x²(x+5)+3(x+5)=0

(x+5)(x²+3)=0

x=-5

Answer 2

x²(x-2)-(x-2)=0

(x-2)(x²-1)=0

(x-2)(x-1)(x+1)=0

x=2 v x=1 v x=-1

b)

x²(x+5)+3(x+5)=0

(x+5)(x²+3)=0

x=-5

 

dla x²+3=0 nie ma pierwiastkow (Δ<0)