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Cubic Equation with integer solution watch

1. 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
2. Usually the solutions would be a factor of d
3. (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.
4. (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?
5. 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.
6. (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
7. (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

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