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

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

Jharkhand CECEJharkhand CECE 2015

Solution:

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) $