Algebra Level pending

If the zeroes of the quadratic polynomial $$f(x)=x^{2}+bx+c$$ are prime numbers such that the $$x$$-coordinate of vertex of curve of $$y=x^2+bx+c$$ is not an integer. And if $$f(7)>0$$ and $$4(5+b)+c<4$$, then find the values of $$b$$ and $$c$$.

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