Algebra

We can use the quadratic formula:

 

$\frac{-17\pm\sqrt{289-88}}{4}$ are the roots. $ab=\frac{-17+\sqrt{289-88}}{4}\cdot\frac{-17-\sqrt{289-88}}{4}=\frac{289-201}{16}=\frac{11}2$

$a+b=\frac{-17+\sqrt{289-88}}{4}+\frac{-17-\sqrt{289-88}}{4}=-\frac{17}2$

$ab+a+b=\frac{11-17}{2}=\boxed{-3}$