The integral values of $a$ for which the quadratic  equation

(x – a) (x – 10) + 1 = 0 has integeral roots are 

If x is an integer and

$(x-a)(x-10)=-1$

$\Rightarrow x-10=1\text{ and }x-a=-1\text{ or }x-10=-1\text{ and }$

$x – a = 1$

$\Rightarrow x=11\text{ and }a=x+1=12\text{ or }x=9\text{ and }a=$

$x – 1 = 8$