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Let-P-C-X-p-x-2-1-p-2-x-1-p-0-0-determin-all-polynom-

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Question Number 203975 by witcher3 last updated on 03/Feb/24
Let P∈C[X] p(x^2 +1)=p^2 (x)+1 p(0)=0 determin all polynom
LetP∈C[X]p(x2+1)=p2(x)+1p(0)=0determinallpolynom
Commented by Rasheed.Sindhi last updated on 03/Feb/24
Let p(x)=ax+b p(0)=b=0 p(x)=ax p(x^2 +1)=a(x^2 +1)=ax^2 +a p^2 (x)+1=(ax)^2 +1=a^2 x^2 +1 ax^2 +a=a^2 x^2 +1 a^2 x^2 −ax^2 =a−1 ax^2 (a−1)=a−1 ax^2 (a−1)−(a−1)=0 (a−1)(ax^2 −1)=0 a=1 ∣ ax^2 =1 One of the solutions is: p(x)=x
Letp(x)=ax+bp(0)=b=0p(x)=axp(x2+1)=a(x2+1)=ax2+ap2(x)+1=(ax)2+1=a2x2+1ax2+a=a2x2+1a2x2−ax2=a−1ax2(a−1)=a−1ax2(a−1)−(a−1)=0(a−1)(ax2−1)=0a=1∣ax2=1Oneofthesolutionsis:p(x)=x

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