SOLUTION: what is the solution set in form of a+bi of 5x^4-320x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: what is the solution set in form of a+bi of 5x^4-320x      Log On


   

Question 942734: what is the solution set in form of a+bi of 5x^4-320x
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you mean,
5x%5E4-320x=0
5x%28x%5E3-64%29=0
Recognize that the second term is the difference of two cubes,
a%5E3+%96+b%5E3+=+%28a+%96+b%29%28a%5E2+%2B+ab+%2B+b%5E2%29
x%5E3-64=%28x-4%29%28x%5E2%2B4x%2B16%29
So,
5x%28x-4%29%28x%5E2%2B4x%2B16%29=0
Two real solutions are,
x=0
and
x-4=0
x=4
and the complex roots,
x%5E2%2B4x%2B16=0
x%5E2%2B4x%2B4%2B12=0
%28x%2B2%29%5E2=-12
x%2B2=0+%2B-+sqrt%28-12%29
x=-2+%2B-+2sqrt%283%29i