Find all real values of the parameter a for which the equation $x^4+2ax^3+x^2+2ax+1=0$ has Find all real values of the parameter a for which the equation $x^4+2ax^3+x^2+2ax+1=0$ has
1) exactly two distinct negative roots
2) at least two distinct negative roots
I tried to factorize it but didn't get any breakthrough.

Hint: Try $x^4+2ax^3+x^2+2ax+1=(x^2+bx+1)(x^2+cx+1)$.
