Question 1151674

{{{f(x)= x^3-1 }}}

{{{f(x)= (x - 1) (x^2 + x + 1)}}}...set {{{f(x)=0}}}

{{{ (x - 1) (x^2 + x + 1)=0}}}=> real zero is {{{x=1}}}


if {{{(x^2 + x + 1)=0}}}.......use quadratic formula


{{{x = (-1 +- sqrt( 1^2-4*1*1 ))/(2*1) }}}

{{{x = (-1 +- sqrt( 1-4))/2 }}}

{{{x = (-1 +- sqrt( -3))/2 }}}


{{{x = (-1 +- (sqrt(-1)*sqrt( 3)))/2 }}}


{{{x = (-1 +- i*sqrt( 3))/2 }}}




complex solutions:

{{{x = (-1 + i*sqrt( 3))/2 }}} =>{{{x = -1/2 + i*sqrt( 3)/2 }}}

{{{x = (-1 - i*sqrt( 3))/2 }}} =>{{{x = -1/2 - i*sqrt( 3)/2 }}}