For what value of c in the equation x^2 + c does the orbit of zero land on a cycle of period 4?

this is discreet dynamics. I do know what values of c make the orbit of zero tend to a cycle of period 4, but i can't figure out when it is part of a 4-cycle.





i need to solve this equation for c so that x=0 is a solution





((((x^2 + c)^2 +c)^2 + c)^2 + c) - x = 0





I don't really know how to solve polynomials of degree 8





I'm kind of confused here. any help would help...

For what value of c in the equation x^2 + c does the orbit of zero land on a cycle of period 4?
If x must be 0,


(((c^2 + c)^2 + c)^2 + c)^2 + c = 0


Rather than expand this and then attempt to factor or iterate a solution, iterate as it stands.


The only non-zero solution appears to be


c = - 1.985424253
Reply:Sorry, that's way above me. Good luck.