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Zetta Paper 1 · Q20

Paper 1Algebra

Given that

f(x)=x2008−2x2007+3x2006−4x2005+⋯+2007x2−2008x+2009f(x)=x^{2008}-2x^{2007}+3x^{2006}-4x^{2005}+\cdots+2007x^2-2008x+2009

and that

g(x)=2012x+2009(1+x)2,g(x)=\frac{2012x+2009}{(1+x)^2},

which of the following is a solution to g(x)=f(x)g(x)=f(x)?

A11
B21/20092^{1/2009}
C31/20093^{1/2009}
D41/20094^{1/2009}
E21/20082^{1/2008}
F31/20083^{1/2008}
G41/20084^{1/2008}

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