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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
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B
12,10
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C
12,8
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D
18,10
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Solution

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 $$a=12$$.

Quantitative Aptitude

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