Question

For what polynomials does this relationship hold:

Answer 1

\[f(x^2)+f(x)f(x+1) = 0\]

Answer 2

hint: The roots may be complex, so try using the modulus of the roots

Answer 3

Here is another hint:
try to find all of the roots of polynomials that satisfy this equation

Answer 4

does anyone have any ideas?

Answer 5

if not, I will give another hint

Answer 6

Hint:
if a is a root, then what is a^2?