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How many roots does the equation x^3 = -1 have.

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lxsptter | Student, Undergraduate | Valedictorian

Posted July 14, 2013 at 6:30 PM via web

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How many roots does the equation x^3 = -1 have.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 14, 2013 at 6:34 PM (Answer #1)

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The equation that is given is x^3 = -1 which is a cubic equation.

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 given equation has 3 roots, two of which are complex and the third is real.

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