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.) x4 − 9x2 + 20 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> 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.) x4 − 9x2 + 20 = 0      Log On


   

Question 705145: 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.)
x4 − 9x2 + 20 = 0
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
It's factorable so that makes the solution simpler to do.

You are probably trying to show x%5E4-9x%5E2%2B20=0. First part is to treat x^2 as the main variable. Factoring gives us:
%28x%5E2-4%29%2A%28x%5E2-5%29=0.
Still not done.

The first binomial factor, to be zero, requires x=-2 or x=+2.

The second binomial would factor to %28x-sqrt%285%29%29%2A%28x%2Bsqrt%285%29%29, so for this to be zero, x=%2Bsqrt%285%29 or x=-sqrt%285%29.

Solution list: -2, -sqrt%285%29, %2B2, %2Bsqrt%285%29.