Question

All the integral values of $a$ for which the quadratic equation $(x-a)(x-10)+1=0$ has integral roots, are

• A. $11,12$
• B. $9,12$
• C. $8,12$
• D. $8,11$

Answer 1

The correct option is C $8,12$

$(x-a)(x-10)=-1;$ where $x,a\in Z$
The product of two integers is $-1$.
$\therefore x-a=1$ and $x-10=-1$
or $x-a=-1$ and $x-10=1$

If $x-10=-1$, then $x=9$
$\Rightarrow a=8$
If $x-10=1$, then $x=11$
$\Rightarrow a=12$