Somebody gave me the following question, I was able to solve it but was unsure about some of the assumptions involved.(adsbygoogle = window.adsbygoogle || []).push({});

Question : Given that the polynomialx^3 + m x^2 + 15 x - 7has at least two rational roots then findm.

Now the questiondidn'tstate thatmhad 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 is7then two rational roots implies that the third root is also rational.

2. Iassumedthatmwas 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 give7I easily found the possible roots of7, 1, 1, that multiply to give7and also have sum of pair-products totalling to15.

4. Som = -(7 + 1 + 1) = -9

So did I need to assume thatmwas integer or could it have been deduced?

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# Polynomial Question

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