SOLUTION: Find all real and complex roots. x^4-9x^2+20=0 -The solution set is { }. (Use a comma to separate answers as needed. Type an exact answer, using radicals as needed. Type co

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find all real and complex roots. x^4-9x^2+20=0 -The solution set is { }. (Use a comma to separate answers as needed. Type an exact answer, using radicals as needed. Type co      Log On


   



Question 969612: Find all real and complex roots.
x^4-9x^2+20=0
-The solution set is { }.
(Use a comma to separate answers as needed. Type an exact answer, using radicals as needed. Type complex answers in the form a + bi.)

Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find all real and complex roots.
x^4-9x^2+20=0
=========================
%28x%5E2+-+5%29%2A%28x%5E2+-+4%29+=+0
Can you do the rest?

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
I would factor into
(x^2-5)(X^2-4)=0. It is just like factoring a quadratic, only you end up with quadratic roots.
x^2-5=0 x^2=5 x=plus sqrt(5) and minus sqrt (5)
x^2-4=0
(x+2)(x-2)=0 Difference of squares.
x=2,-2
The four roots are -sqrt (5), -2, 2, and sqrt (5)
+graph%28300%2C200%2C-3%2C3%2C-5%2C30%2Cx%5E4-9x%5E2%2B20%29