SOLUTION: Find all solutions, real and complex, of the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) x^3 + 4x^2 + 16x + 64 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find all solutions, real and complex, of the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) x^3 + 4x^2 + 16x + 64 = 0       Log On


   

Question 898498: Find all solutions, real and complex, of the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
x^3 + 4x^2 + 16x + 64 = 0
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Try testing the roots, plus-or-minus 2, 4, 8, using synthetic division. You should find -4 is a root, so your polynomial is %28x%2B4%29%28x%5E2%2B16%29=0. The quadratic factor will have complex roots with an imaginary number. They are x=-4i and x=4i.