If If $x^2+ax+b+1=0$ has roots which are positive integers, then $(a^2+b^2)$ can be which of the given choices? 
If $x^2+ax+b+1=0$ has roots which are positive integers, then $(a^2+b^2)$ can be
(A) 50
(B) 37
(C) 19
(D) 61

My approach: I first took roots $\alpha$, $\beta$ and then applied sum and product of roots according to Vieta's formula. But I don't think we can get any value with that. Any help will be much appreciation.
Also can we actually find the range of $a^2+b^2$.

We need that $a$ and $b$ will be naturals and there is a natural $n$ for which $$a^2-4(b+1)=n^2.$$
Thus, $$a^2+b^2=n^2+b^2+4b+4=n^2+(b+2)^2.$$
Can you end it now?
