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prove $q_1t^3+(k_2-1)t^2-k_2((q_1^2-1)k_1+1)^2=0$ has no Positive integer root, t is variable , $q_1$ is constant and $k_1,k_2$ are parameter
$q_1>0, k_1>0, k_2>0$, and all characters represent positive integers, it's important for my one question, I hope someone can give me a correct answer and this isn't a homework, so I hope administrator doesn't shut down the question.

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it never mind if it is homework: you can still ask and people will still try to help. Nevertheless, if it is homework then tag your question as such so that people know that you're more or less a beginner in the subject. – DonAntonio Dec 6 '12 at 12:56
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Try it for q1 = k1 = k2 = 1. Maybe I am misunderstanding your specification in some way. Otherwise, you can put into one of the cubic forms and work out a solution, see: mathworld.wolfram.com/CubicFormula.html – Amzoti Dec 6 '12 at 13:35
@Amzoti I think you mean $-q_1=k_1=k_2=1$? – awllower Dec 6 '12 at 13:55
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@awllower Correct, I have been remiss in MathJax, thank you (note that that is a dash in your response and should not be confused by negative as the OP may not be familiar with the subtleties of our language.) – Amzoti Dec 6 '12 at 14:00

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