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What is the sum of the roots for the equation x^3 = 1.

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lxsptter | Student, Undergraduate | Valedictorian

Posted July 14, 2013 at 6:24 PM via web

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What is the sum of the roots for the equation x^3 = 1.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 14, 2013 at 6:29 PM (Answer #1)

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The equation that is given is `x^3 = 1` .

`x^3 = 1`

=> `x^3 - 1 = 0`

=> `(x-1)*(x^2+x+1) = 0`

x - 1 = 0

=> x = 1

x^2 + x + 1 = 0

=> x = `(-1 - sqrt(1 - 4))/2` and x = `(-1 + sqrt(1 - 4))/2`

=> x = `-1/2 - i*sqrt 3/2` and x = `-1/2 + i*sqrt 3/2`

The roots of the equation are `{1, -1/2 - i*sqrt 3/2, x = -1/2 + i*sqrt 3/2}.`

The sum of the roots is `1+ (-1/2 - i*sqrt 3/2)+(-1/2 + i*sqrt 3/2) = 0`

The required sum of the roots is 0

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