- Thread starter
- Admin
- #1
- Feb 14, 2012
- 3,967
For some integer $k$, the polynomial $x^3-2011x+k$ has three integer roots $p, q, r$. Evaluate $ |p|+|q|+|r|$.
Hello.For some integer $k$, the polynomial $x^3-2011x+k$ has three integer roots $p, q, r$. Evaluate $ |p|+|q|+|r|$.
I am sorry, mente oscura because that isn't the correct answer.Hello.
I do not know if I have interpreted the question well.
[tex]p+q+r=0[/tex]
Regards.
@Opalg, $(p, q, r) = (49, 39, -88)$ does not seem to yield a $k$ such that the cubic is separable over $\mathbb{Z}[x]$, let alone being each of $p, q$ and $r$ a root.
Sorry you're not well. I hope you recover in time for Christmas.Hey MHB,
I will reply to this thread after I gained much more energy, because now I am very sick and ill with symptoms including stomach pain, vomiting, diarrhea and nausea.
A little birdie told me she has seen her doctor, taken some prescribed medicine, and is feeling much better now.Sorry you're not well. I hope you recover in time for Christmas.
I am not quite convinced that some "little birdie" told you that muchMarkFL said:A little birdie told me ...
sorry to hear itHey MHB,
I will reply to this thread after I gained much more energy, because now I am very sick and ill with symptoms including stomach pain, vomiting, diarrhea and nausea.
Sorry guys!
Thank you so much Opalg for participating, yes, your second attempt is correct, well done, Opalg!Yes, I got a sign wrong (you can probably see where).
It should have been $(2p+q)^2 + 3q^2 = 8044$, and the result of that is $p=10$, $q=39$, and therefore $r=-49$, so that $|p| + |q| + |r| = 98$. The value of $k$ is then $-pqr = 19\,110$. Better?
I am very sorry to hear that, hope you get better soon.![]()
Sorry you're not well. I hope you recover in time for Christmas.
Thank you so much for yours concern, as Mark has already mentioned, I felt much better after taking the medicines, but I am not feeling completely okay yet, because I vomited last midnight but I am positively that I will be okay after finishing all of the prescribed medicines.sorry to hear it
take care of yourself please ,and hope you will get better soon