How do you find all the complex roots of x^3-x^2+x-1?

1 Answer
Feb 19, 2016

x = 1 , i , -i

Explanation:

Step 1: Set the equation to equal to zero

x^3-x^2+x-1= 0

Step 2: Group the terms like this

color (red)((x^3-x^2)) + color(blue)((x-1)) = 0

Step 3: Factor out the common like term for each group

x^2color(red)((x-1)) + 1color(red)((x-1)) = 0
(x^2 +1)(x-1) = 0

Step 4 Set each factor equal to zero

x^2 +1" " = 0
" " -1 " " " " -1
x^2" " " = " " -1
sqrt(x^2) " " = sqrt(-1)

x = +- i

or

x-1= 0
x = 1

Answer: x = 1 , i , -i