SOLUTION: Hi - I am having some trouble understanding "higher degree polynomial equations" Can you please help me solve this, and show me how: 4x^4 - 2x^2 - 4 = 2 Thank you!!!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi - I am having some trouble understanding "higher degree polynomial equations" Can you please help me solve this, and show me how: 4x^4 - 2x^2 - 4 = 2 Thank you!!!      Log On


   

Question 427846: Hi - I am having some trouble understanding "higher degree polynomial equations" Can you please help me solve this, and show me how:
4x^4 - 2x^2 - 4 = 2
Thank you!!!
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let z+=+x%5E2 so our quartic equation becomes 4z%5E2+-+2z+-+4+=+2 --> 4z%5E2+-+2z+-+6+=+0 --> 2z%5E2+-+z+-+3+=+0. This factors to %282z+-+3%29%28z+%2B+1%29+=+0, so either z+=+3%2F2 or z+=+-1. Substituting back into our expression for z in terms of x, we obtain
x%5E2+=+3%2F2 --> x+=+sqrt%283%2F2%29, x+=+-sqrt%283%2F2%29
x%5E2+=+-1 --> x+=+i, x+=+-i (i is the imaginary unit, equal to sqrt%28-1%29.