An algebra problem by sunny chaturvedi

Algebra Level 3

If f ( x ) f(x) is a polynomial such that f ( x + 1 ) = f ( x ) + 2 x + 1 f(x+1)=f(x)+2x+1 , and f ( 0 ) = 1 f(0)=1 , then find f ( 2017 ) f(2017) .

2018 2017*2016/2 2017^2+1 2018^2+1 2017^2

Sunny Chaturvedi by sunny chaturvedi , 21, India

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1 solution

Vilakshan Gupta
Aug 27, 2017

Observing the pattern by putting first few values of x x , we get that f ( n ) = n 2 + 1 f(n)=n^2+1

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