2. Given $p+q=96$, and the quadratic equation $x^{2}+p x$ $+q=0$ has integer roots. Then its largest root is
2. 98 .

Let the two roots be $x_{1}$ and $x_{2}$. Then $96=(x_{1}-1)(x_{2}-1)-1$, so $(x_{1}-1)(x_{2}-1)=97$. Since 97 is a prime number, then $x_{1}-1= \pm 1$, $x_{2}-1= \pm 97$, hence the largest root is 98.