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

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Answer 1 · 2016-02-19T19:37:49

# x = 1 , i , -i#

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#