SOLUTION: Can you please help me solve this? I have to solve for all roots. {{{x^4-5x^2-24=0}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you please help me solve this? I have to solve for all roots. {{{x^4-5x^2-24=0}}}      Log On


   

Question 189607: Can you please help me solve this? I have to solve for all roots. x%5E4-5x%5E2-24=0
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
x%5E4-5x%5E2-24+=+0
You can write this as a quadratic equation with a temporary change of variable, thus...
Let y+=+x%5E2 so that x%5E4+=+y%5E2, then you substitute...
y%5E2-5y-24+=+0 Factor this...
%28y-8%29%28y%2B3%29+=+0 Apply the zero product rule:
y-8+=+0 or y%2B3+=+0 so that...
y+=+8 or y+=+-3 Now substitue back y+=+x%5E2 so you have...
x%5E2+=+8 or x%5E2+=+-3 and...
x+=+sqrt%288%29, x+=+-sqrt%288%29 or x+=+sqrt%28-3%29, x+=+-sqrt%28-3%29
The roots are:
x+=+sqrt%288%29
x+=+-sqrt%288%29
x+=+sqrt%283%29i
x+=+-sqrt%283%29i where: i+=+sqrt%28-1%29