A problem ask to find the constants $a$, $b$ and $c$ if $f(z)=az^2+bz+c$ and $\int_{\gamma}\frac{f(z)}{z}dz=2 \pi i$, $\int_{\gamma}\frac{f(z)}{z+1}dz=4 \pi i$ and $\int_{\gamma}\frac{f(z)}{z-1}dz=8 \pi i$ where the contour is $\gamma = C(0,2)$
So I obtain the system of equations in using the Cauchy theorem $$1=c$$ $$2=a-b+1$$ $$4=a+b+1$$ $$\implies f(z) = 2z^2+z+1$$ Am I right? Otherwise, What do I have to change my answer for it to be true?