Question

If $a\in$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. $18,10$

Answer 1

The correct option is C $12,8$

Since, $a$ and $x$ are integers.
Therefore, $(x-a)(x-10)+1=0$
$\Rightarrow (x-a)(x-10)=-1$
$\Rightarrow x-a=1$ and $x-10=-1$
or $x-a=-1$ and $x-10=1$
$\Rightarrow x=9$ and $a=8$ or $x=11$ and $a=12$
$\Rightarrow a=8$ or $a=12$.