Relation Between quadratic equation coefficient and polynomial value [on hold]
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
$2A$ ,$A+B$ are integer but $C$ may not be
$A+B$ ,$C$ are integer but $2A$ may not be
$A+B$ ,$C$, $2A$ all integer.
Can't find any specific relation or how to proceed.
quadratics quadratic-forms quadratic-residues
asked yesterday
Debayan Bairagi
1
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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
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
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
$2A$ ,$A+B$ are integer but $C$ may not be
$A+B$ ,$C$ are integer but $2A$ may not be
$A+B$ ,$C$, $2A$ all integer.
Can't find any specific relation or how to proceed.
quadratics quadratic-forms quadratic-residues
asked yesterday
Debayan Bairagi
1
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
add a comment |
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
$2A$ ,$A+B$ are integer but $C$ may not be
$A+B$ ,$C$ are integer but $2A$ may not be
$A+B$ ,$C$, $2A$ all integer.
Can't find any specific relation or how to proceed.
quadratics quadratic-forms quadratic-residues
asked yesterday
Debayan Bairagi
1
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
$2A$ ,$A+B$ are integer but $C$ may not be
$A+B$ ,$C$ are integer but $2A$ may not be
$A+B$ ,$C$, $2A$ all integer.
Can't find any specific relation or how to proceed.
quadratics quadratic-forms quadratic-residues
quadratics quadratic-forms quadratic-residues
asked yesterday
Debayan Bairagi
1
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
1
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
1
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
1
asked yesterday
Debayan Bairagi
1
1
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.
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
add a comment |
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
add a comment |
1 Answer
1
active
oldest
votes
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.
answered 23 hours ago
James
703115
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
answered 23 hours ago
James
703115
add a comment |
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.
answered 23 hours ago
James
703115
add a comment |
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.
answered 23 hours ago
James
703115
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.
answered 23 hours ago
James
703115
answered 23 hours ago
James
703115
answered 23 hours ago
James
703115
answered 23 hours ago
James
703115
703115
add a comment |
add a comment |
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