SOLUTION: Find the solutions of the equation. x^3-125= 0 x^3= 125 x= 5 How can I find the COMPLEX solutions? I believe you have to use the quadratic equation but I'm not really sure

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the solutions of the equation. x^3-125= 0 x^3= 125 x= 5 How can I find the COMPLEX solutions? I believe you have to use the quadratic equation but I'm not really sure       Log On


   

Question 344305: Find the solutions of the equation.
x^3-125= 0
x^3= 125 x= 5
How can I find the COMPLEX solutions? I believe you have to use the quadratic equation but I'm not really sure how to factor x^3-125.
Thanks!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
No, you can't use the quadratic formula on a cubic equation.
Recognize that this is the difference of two cubes.
x%5E3-125=%28x-5%29%28x%5E2%2B5x%2B25%29=0
One solution is x-5=0
highlight%28x=5%29
.
.
.
Now find the root of the quadratic equation with the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A25+%29%29%2F2+
x+=+%28-5+%2B-+sqrt%28+25-100+%29%29%2F2+
x+=+%28-5+%2B-+sqrt%28+-75%29+%29%29%2F2+
highlight%28x+=+%285%2F2%29%28-1+%2B-+sqrt%28+3+%29i%29%29+ where i=sqrt%28-1%29