P-o-1-P-1-1-X-and-for-all-n-1-P-n-1-P-n-XP-n-1-Explicit-P-n-and-prove-that-its-roots-are-all-real-

Question Number 125736 by snipers237 last updated on 13/Dec/20

P_{o} = 1, P_{1} = 1 + X a n d f o r a l l n ⩾ 1

P_{n + 1} = P_{n} + {X P}_{n - 1}

E x p l i c i t P_{n} a n d p r o v e t h a t i t s r o o t s a r e a l l r e a l .