Polynomially Yours!

Algebra Level 4

If $$f(x)=x^{2}+bx+c$$ where $$b,c$$ are integers and it is given that $$f(x)$$ perfectly divides $$x^{4}+6x^{2}+25$$ and $$3x^{4}+4x^{2}+28x+5$$, what is the value of $$f(1)?$$

Note-This question is taken from SOF-IMO

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