Answer:
Roots: 2, 2i, -2i
Step-by-step explanation:
[tex]f(m)=m^3-2m^2+4m-8[/tex]
Set the expression equal to zero:
[tex]m^3-2m^2+4m-8=0[/tex]
Factor out common terms:
[tex]m^2(m-2)+4(m-2)=0[/tex]
Factor out (m-2):
[tex](m-2)(m^2+4)=0[/tex]
This equation will be true when either one of the multiplicands is equal to 0. Write 2 equations and solve:
[tex]m-2=0\\m=2[/tex]
[tex]m^2+4=0\\m^2=-4\\m=2i, -2i[/tex]
Roots: 2, 2i, -2i
