SOLUTION: please help me solve this equation 3x^4-11x^2-20=0

Algebra ->  Rational-functions -> SOLUTION: please help me solve this equation 3x^4-11x^2-20=0      Log On


   



Question 575503: please help me solve this equation
3x^4-11x^2-20=0

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Sometimes it simpifies things a bit by temporarily using a substitute variable:
Temporarily let x%5E2+=+y so now you have:
3y%5E2-11y-20+=+0 Factor:
%283y%2B4%29%28y-5%29+=+0 Solve for y:
3y%2B4+=+0 or y-5+=+0 so...
y+=+-4%2F3 or y+=+5 Replace y+=+x%5E2 to get...
x%5E2+=+-4%2F3 or x%5E2+=+5 Taking the square roots, we get...
x+=+sqrt%28-4%2F3%29 or x+=+-sqrt%28-4%2F3%29 or x+=+sqrt%285%29 or x+=+-sqrt%285%29
If you need your answers in approximate form, then...
x+=+2.236 or x+=+-2.236 or x+=+1.155i or x+=+-1.155i
Here's what the graph looks like:
graph%28400%2C400%2C-5%2C5%2C-30%2C5%2C3x%5E4-11x%5E2-20%29