Integer roots to cubic equation

Question

If I have a cubic equation $x^3 + ax^2 + bx + c = 0$, what constraints exist on $a,b,c$ when we have three integer solutions?

How do I choose $a,b,c$ to force integer solutions?

Answer 1

Hint:

Use the Rational Root Theorem.

Answer 2

• Vieta's formulas (http://en.wikipedia.org/wiki/Vieta's_formulas)
• every root is a factor of c