If a∈ Z and the equation (x-a)(x-10)+1=0 has integral roots, then the values of a are

Question

If a∈ 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

Tardigrade Admin · Accepted Answer

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

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

$10, 8$

$12, 10$

$12, 8$

$18, 10$

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

Q. If a∈Z and the equation (x−a)(x−10)+1=0 has integral roots, then the values of a are

10,8

12,10

12,8

18,10