Question

Fie poinomul f=x^3-3x+m ,f apartineR cu radacinile complexe x1,x2,x3. Determinati radacinile polinomului pt m=2

Answer 1

f=x³-3x+2=(x³-x)+(-2x+2)=
x(x²-1)-2(x-1)=x(x-1)(x+1)-2(x-1)=
(x-1)[x(x-1)-2]=
(x-1)(x²-x-2)=0
x-1=0=>x1=1
x²-x-2=0
Δ=1+4*2=1+8=9
x2=(1-√9)/2=-2/2=-1
x3=(1+√9)/2=4/2=2
S={-1,1,2}