Somebody gave me the following question, I was able to solve it but was unsure about some of the assumptions involved. Question : Given that the polynomial x^3 + m x^2 + 15 x - 7 has at least two rational roots then find m. Now the question didn't state that m had to be integer and I was unsure as to whether this was meant to be assumed or whether it could be deduced. Here's what I did. 1. Since the product of the roots is 7 then two rational roots implies that the third root is also rational. 2. I assumed that m was integer which meant that the rational roots where also integer. ( by the http://planetmath.org/encyclopedia/RationalRootTheorem.html [Broken] ) 3. Since there are very few ways of having integer roots that multiply to give 7 I easily found the possible roots of 7, 1, 1, that multiply to give 7 and also have sum of pair-products totalling to 15. 4. So m = -(7 + 1 + 1) = -9 So did I need to assume that m was integer or could it have been deduced?