Question

lf $a\in Z$ and the equation $(x-a)(x-10)+1=0$ has integral roots, then the values of $a$ are

• A. $10,8$
• B. $12,10$
• C. $12,8$
• D. $10,12$

Answer 1

The correct option is C $12,8$

The given equation is $(x-a)(x-10)+1=0$
$\Rightarrow (x-a)(x-10)=-1$
$\because (x,a)\in Z$
Either
$x-a=+1$ and $x-10=-1$
$\Rightarrow x=9$ and $a=8$
Or
$(x-a)=-1$ and $(x-10)=+1$
$\Rightarrow x=11$ and $a=12$
$\therefore (x,a)=(9,8)$ or $(x,a)=(11,12)$
$\Rightarrow a=(8,12)$
Hence, option C.