Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    10
    ReputationRep:
    Is there a way can restrict the values of a,b,c,d (ax^3+bx^2+cx+d) to get a cubic equation with integer solutions? Or any other way to do that
    Offline

    8
    ReputationRep:
    Usually the solutions would be a factor of d
    • Study Helper
    Offline

    13
    (Original post by 214508)
    Is there a way can restrict the values of a,b,c,d (ax^3+bx^2+cx+d) to get a cubic equation with integer solutions? Or any other way to do that
    Depending on what you're trying to do, you could work in reverse.

    Say you want a cubic whose roots are 1,2,3.

    then a(x-1)(x-2)(x-3) is our desired cubic, where a is any non-zero number. Expand and you have it in the form given in your question.
    Offline

    13
    ReputationRep:
    (Original post by 214508)
    Is there a way can restrict the values of a,b,c,d (ax^3+bx^2+cx+d) to get a cubic equation with integer solutions? Or any other way to do that
    Possibly I haven't woken up yet, but this seems to be quite a hard question. See for example:

    https://arxiv.org/ftp/arxiv/papers/1110/1110.6110.pdf

    Where have you come across this question?
    Offline

    18
    ReputationRep:
    Not sure if it's needed here, but it might be helpful to know that the sum of the roots of a cubic equation equal -b/a (where a is the x^3 coefficient and b is the x^2 coefficient), the sum of the roots in pairs (that's pq + pr + qr where p, q and r are the roots) is c/a and the product of the roots is -d/a.
    • Thread Starter
    Offline

    10
    ReputationRep:
    (Original post by Gregorius)
    Possibly I haven't woken up yet, but this seems to be quite a hard question. See for example:

    https://arxiv.org/ftp/arxiv/papers/1110/1110.6110.pdf

    Where have you come across this question?
    I am studying Computer Science , so while programming I was trying to make a program to make a cubic equation and then solve it as well, but I only want to work with integer roots
    Offline

    8
    ReputationRep:
    (Original post by 214508)
    I am studying Computer Science , so while programming I was trying to make a program to make a cubic equation and then solve it as well, but I only want to work with integer roots
    Just use the cubic formula
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Will you be richer or poorer than your parents?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.