Solution:
The given equation is (x−a)(x−10)+1=0⇒(x−a)(x−10)=−1
∵(x, a)∈Z
So,
x−a=1 and x−10=−1
⇒x=9 and a=8
or
(x−a)=−1 and (x−10)=+1
⇒x=11 and a=12
∴(x,a)=(9,8) or (x,a)=(11,12)
⇒a=(8,12)
option 3 is correct.
Mathematicslf a∈Z and the equation (x−a) (x−10) +1=0 has integral roots, then the values of a are,
lf a∈Z and the equation (x−a) (x−10) +1=0 has integral roots, then the values of a are,
⇒(x−a)(x−10)=−1
∵(x, a)∈Z
So,
x−a=1 and x−10=−1
⇒x=9 and a=8
or
(x−a)=−1 and (x−10)=+1
⇒x=11 and a=12
∴(x,a)=(9,8) or (x,a)=(11,12)
⇒a=(8,12)
option 3 is correct.
