Question 927772

{{{ x^2-2x+13=0 }}}...use quadratic formula to find roots


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


{{{x = (-(-2)+- sqrt( (-2)^2-4*1*13 ))/(2*1) }}}



{{{x = (2+- sqrt(4-52))/2 }}}


{{{x = (2+- sqrt(-48))/2 }}}

{{{x = (2+- sqrt((-1)48))/2 }}}

{{{x = (2+- 6.93*i)/2 }}}

complex solutions (means there is no x-intercepts):


{{{x = (2+ 6.93*i)/2 }}}

{{{x = 2/2+ (6.93*i)/2 }}}

{{{x = 1+ 3.465*i }}}

or

{{{x = (2-6.93*i)/2 }}}

{{{x = 2/2-(6.93*i)/2 }}}

{{{x = 1-3.465*i }}}


the sum of the cubes of the roots will be: 

{{{(1+ 3.465*i)^3+(1- 3.465*i)^3}}}

{{{(1+ 3.465*i)(1+ 3.465*i)(1+ 3.465*i)+(1- 3.465*i)(1- 3.465*i)(1- 3.465*i)}}}

{{{-35.0187-31.2066i-35.0187+31.2066i}}}

{{{-35.0187-cross(31.2066i)-35.0187+cross(31.2066i)}}}

{{{-70.0374}}}