Find the all the roots of the polynomial x4 + x2 + 1.
The above is from an example in a text book. I attempted the question and solved it (I think) by
letting u = x2
then solving the rewritten polynomial u2 + u + 1 using the quadratic formula before solving for x.
I get the roots,
But the book's author use completing the square to obtain the factors (x 2 + x + 1)(x2 - x + 1)
Which he then proceeds to solve using the quadratic formula to obtain
My question is, why the different answers? Am I doing it wrong? That would be ironic because I learned that substitution trick from the very same book. Or is there something am missing?