SOLUTION: how do you find the complex zeros of the polynomial function. f(x)=x^3 + 125

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: how do you find the complex zeros of the polynomial function. f(x)=x^3 + 125      Log On


   

Question 890111: how do you find the complex zeros of the polynomial function.
f(x)=x^3 + 125
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Either factor the expression or use Rational Roots Theorem. You have the sum of cubes.

x%5E3%2B125=x%5E3%2B5%5E3=%28x%2B5%29%28x%5E2-5x%2B5%5E2%29

Check the quadratic factor for the roots of +- 1, +-5, or +- 25. You can instead, just find its roots using the general solution to quadratic formula.

x=%285%2B-+sqrt%2825-4%2A25%29%29%2F%282%29
x=%285%2B-+sqrt%28-75%29%29%2F2
x=5%2F2%2B-+%281%2F2%29%2A5sqrt%28-3%29
highlight%28x=5%2F2%2B-+%285%2F2%29i%2Asqrt%283%29%29---these are TWO of the roots.

Obviously the first root is highlight%28x=-5%29.