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-

Tinku Tara June 4, 2023 Differentiation 0 Comments

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

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.

$${P}_{{o}} =\mathrm{1}\:\:,{P}_{\mathrm{1}} =\mathrm{1}+{X}\:{and}\:{for}\:{all}\:{n}\geqslant\mathrm{1} \\ $$$${P}_{{n}+\mathrm{1}} ={P}_{{n}} +{XP}_{{n}−\mathrm{1}} \: \\ $$$${Explicit}\:\:{P}_{{n}} \:\:{and}\:{prove}\:{that}\:{its}\:{roots}\:{are}\:{all}\:{real}. \\ $$

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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-

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