Question

Algebraically determine the roots of f(m)=m^3-2m^2+4m-8

Answer 1

Answer:

Roots: 2, 2i, -2i

Step-by-step explanation:

$f(m)=m^3-2m^2+4m-8$

Set the expression equal to zero:

$m^3-2m^2+4m-8=0$

Factor out common terms:

$m^2(m-2)+4(m-2)=0$

Factor out (m-2):

$(m-2)(m^2+4)=0$

This equation will be true when either one of the multiplicands is equal to 0. Write 2 equations and solve:

$m-2=0\\m=2$

$m^2+4=0\\m^2=-4\\m=2i, -2i$

Roots: 2, 2i, -2i