0
$\begingroup$

Stuck finding the zeros of this polynomial (complex and real): $$x^4+2x^2+1$$

I am not sure how I would factor this. The constant value is really throwing me off. I just need a hint on how to get that done and I think I have a handle on the rest of it.

|cite|improve this question
$\endgroup$
2
$\begingroup$

set $u = x^2$ and use the quadratic formula to factorize it.

if you do the change, you will have

$u^2 +2u +1$ and from here its easy to solve it, ones you factorize it remember to go back to $x$

|cite|improve this answer
$\endgroup$
  • $\begingroup$ So this is just an expression of the quadratic type and I should treat it as such? $\endgroup$ – Cherry_Developer Sep 22 '14 at 23:39
  • $\begingroup$ yes kind of... but when you do the factorization for $u$ you have to remember to go back to $x$ $\endgroup$ – Jearson Narvaez Rojas Sep 22 '14 at 23:40
0
$\begingroup$

set $u = x^2$ and use the quadratic formula to factorize it.

if you do the chage, you will have

$u^2 +2u +1$ and from here its easy to solve it.

$$u^2 +2u +1 = (u+1)(u+1) = (x^2 +1)(x^2 +1) = (x-i)(x+i)(x-i)(x+i) =(x-i)^{2}(x+i)^{2}$$ and its done

|cite|improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.