A sequence of polynomials starts 0, 1 and each poly is given by
combining the two polys in the sequence just before it. Investigate
and prove results about the roots of the polys.

And So on - and on -and On

Age 16 to 18 Challenge Level

The solution needs you to be systematic.

Start with $ f_{0} $, then work out $ f_{1}$, then work out $
f_{2}$