Relation Between quadratic equation coefficient and polynomial value [on hold]












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If $f(x)=Ax^2+Bx+C$ Where $A, B ,C$ are real. If $f(x)$ is integer whenever $x$ is integer. What will be the relation or characteristic of $A, B, C$ ? Options are





  1. $2A$ ,$A+B$ are integer but $C$ may not be


  2. $A+B$ ,$C$ are integer but $2A$ may not be


  3. $A+B$ ,$C$, $2A$ all integer.


Can't find any specific relation or how to proceed.






quadratics quadratic-forms quadratic-residues







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Debayan Bairagi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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put on hold as off-topic by Martin R, Saad, Adrian Keister, Lee David Chung Lin, John Wayland Bales 17 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Martin R, Saad, Adrian Keister, Lee David Chung Lin, John Wayland Bales

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  • 1) is not possible, since $f(0)=C$ is an integer.
    – James
    23 hours ago






  • 1




    Consider f(0), f(1), and f(-1) ...
    – Martin R
    23 hours ago
















0














If $f(x)=Ax^2+Bx+C$ Where $A, B ,C$ are real. If $f(x)$ is integer whenever $x$ is integer. What will be the relation or characteristic of $A, B, C$ ? Options are





  1. $2A$ ,$A+B$ are integer but $C$ may not be


  2. $A+B$ ,$C$ are integer but $2A$ may not be


  3. $A+B$ ,$C$, $2A$ all integer.


Can't find any specific relation or how to proceed.






quadratics quadratic-forms quadratic-residues







share|cite|improve this question







New contributor




Debayan Bairagi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











put on hold as off-topic by Martin R, Saad, Adrian Keister, Lee David Chung Lin, John Wayland Bales 17 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Martin R, Saad, Adrian Keister, Lee David Chung Lin, John Wayland Bales

If this question can be reworded to fit the rules in the help center, please edit the question.













  • 1) is not possible, since $f(0)=C$ is an integer.
    – James
    23 hours ago






  • 1




    Consider f(0), f(1), and f(-1) ...
    – Martin R
    23 hours ago














0












0








0


1





If $f(x)=Ax^2+Bx+C$ Where $A, B ,C$ are real. If $f(x)$ is integer whenever $x$ is integer. What will be the relation or characteristic of $A, B, C$ ? Options are





  1. $2A$ ,$A+B$ are integer but $C$ may not be


  2. $A+B$ ,$C$ are integer but $2A$ may not be


  3. $A+B$ ,$C$, $2A$ all integer.


Can't find any specific relation or how to proceed.






quadratics quadratic-forms quadratic-residues







share|cite|improve this question







New contributor




Debayan Bairagi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











If $f(x)=Ax^2+Bx+C$ Where $A, B ,C$ are real. If $f(x)$ is integer whenever $x$ is integer. What will be the relation or characteristic of $A, B, C$ ? Options are





  1. $2A$ ,$A+B$ are integer but $C$ may not be


  2. $A+B$ ,$C$ are integer but $2A$ may not be


  3. $A+B$ ,$C$, $2A$ all integer.


Can't find any specific relation or how to proceed.






quadratics quadratic-forms quadratic-residues




quadratics quadratic-forms quadratic-residues






share|cite|improve this question







New contributor




Debayan Bairagi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question







New contributor




Debayan Bairagi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question






New contributor




Debayan Bairagi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked yesterday









Debayan Bairagi

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1




New contributor




Debayan Bairagi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor





Debayan Bairagi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Debayan Bairagi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




put on hold as off-topic by Martin R, Saad, Adrian Keister, Lee David Chung Lin, John Wayland Bales 17 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Martin R, Saad, Adrian Keister, Lee David Chung Lin, John Wayland Bales

If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Martin R, Saad, Adrian Keister, Lee David Chung Lin, John Wayland Bales 17 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Martin R, Saad, Adrian Keister, Lee David Chung Lin, John Wayland Bales

If this question can be reworded to fit the rules in the help center, please edit the question.












  • 1) is not possible, since $f(0)=C$ is an integer.
    – James
    23 hours ago






  • 1




    Consider f(0), f(1), and f(-1) ...
    – Martin R
    23 hours ago


















  • 1) is not possible, since $f(0)=C$ is an integer.
    – James
    23 hours ago






  • 1




    Consider f(0), f(1), and f(-1) ...
    – Martin R
    23 hours ago
















1) is not possible, since $f(0)=C$ is an integer.
– James
23 hours ago




1) is not possible, since $f(0)=C$ is an integer.
– James
23 hours ago




1




1




Consider f(0), f(1), and f(-1) ...
– Martin R
23 hours ago




Consider f(0), f(1), and f(-1) ...
– Martin R
23 hours ago










1 Answer
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1) is wrong, since $f(0)=C$ is an integer. $f(1)=A+B+C$. Since $C$ is an integer, $f(1)-C=A+B$ is an integer, too. $f(-1)=A-B+C=2A-A-B+C$ is an integer, thus $f(-1)+(A+B)-C=2A$ is an integer, 2) is wrong and 3) is correct.






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    1 Answer
    1






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    1 Answer
    1






    active

    oldest

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    active

    oldest

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    active

    oldest

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    1) is wrong, since $f(0)=C$ is an integer. $f(1)=A+B+C$. Since $C$ is an integer, $f(1)-C=A+B$ is an integer, too. $f(-1)=A-B+C=2A-A-B+C$ is an integer, thus $f(-1)+(A+B)-C=2A$ is an integer, 2) is wrong and 3) is correct.






    share|cite|improve this answer


























      0














      1) is wrong, since $f(0)=C$ is an integer. $f(1)=A+B+C$. Since $C$ is an integer, $f(1)-C=A+B$ is an integer, too. $f(-1)=A-B+C=2A-A-B+C$ is an integer, thus $f(-1)+(A+B)-C=2A$ is an integer, 2) is wrong and 3) is correct.






      share|cite|improve this answer
























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        0








        0






        1) is wrong, since $f(0)=C$ is an integer. $f(1)=A+B+C$. Since $C$ is an integer, $f(1)-C=A+B$ is an integer, too. $f(-1)=A-B+C=2A-A-B+C$ is an integer, thus $f(-1)+(A+B)-C=2A$ is an integer, 2) is wrong and 3) is correct.






        share|cite|improve this answer












        1) is wrong, since $f(0)=C$ is an integer. $f(1)=A+B+C$. Since $C$ is an integer, $f(1)-C=A+B$ is an integer, too. $f(-1)=A-B+C=2A-A-B+C$ is an integer, thus $f(-1)+(A+B)-C=2A$ is an integer, 2) is wrong and 3) is correct.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 23 hours ago









        James

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        703115















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