SOLUTION: Find the zeros (or roots) {{{x^3-8=0}}} express complex numbers in terms of i

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the zeros (or roots) {{{x^3-8=0}}} express complex numbers in terms of i      Log On


   

Question 340712: Find the zeros (or roots)
x%5E3-8=0 express complex numbers in terms of i
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Find the zeros (or roots)
x%5E3-8=0 express complex numbers in terms of i

Factor the expression as the difference of cubes:

%28x-2%29%28x%5E2%2B2x%2B4%29=0

Set each factor = 0

Setting x-2=0
Solution: x=2

Setting the second factor = 0:

x%5E2%2B2x%2B4=0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 

x+=+%28-%282%29+%2B-+sqrt%28%282%29%5E2-4%2A%281%29%2A%284%29+%29%29%2F%282%2A%281%29%29+ 

x+=+%28-2+%2B-+sqrt%284-16%29%29%2F2+

x+=+%28-2+%2B-+sqrt%28-12%29%29%2F2+

x+=+%28-2+%2B-+i%2Asqrt%2812%29%29%2F2+

x+=+%28-2+%2B-+i%2Asqrt%284%2A3%29%29%2F2+

x+=+%28-2+%2B-+2i%2Asqrt%283%29%29%2F2+

x+=+%282%28-1+%2B-+i%2Asqrt%283%29%29%29%2F2+

x+=+%28cross%282%29%28-1+%2B-+i%2Asqrt%283%29%29%29%2Fcross%282%29+

x+=+-1+%2B-+i%2Asqrt%283%29+

The three solutions are

x=2, x+=+-1+%2B+i%2Asqrt%283%29+, x+=+-1+-+i%2Asqrt%283%29+



Edwin