Let `a,b,c` be rational numbers and `f:Z->Z` be a function given by `f – InterviewSolution

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1.	Let `a,b,c` be rational numbers and `f:Z->Z` be a function given by `f(x)=a x^2+b x+c.` Then, `a+b` isA. a negative integerB. an integerC. non-integral rational numberD. none of these
Answer» Correct Answer - B Since `f(x) Z to Z` is given by `f(x)=ax^(2)+bx+c" for all x "inZ.` `therefore f(x)=ax^(2)+bc+c` takes integral values for all `x in Z`. `therefore f(x)` is an integer for all `x in Z`. `therefore f(0)` and f(1) are integers `therefore f(1)-f(0)` is an integer. `therefore (a+b+c)-c` is an integer `[therefore f(0)=c and f(1)=a+b+c]` `therefore` a+b is an integer.

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