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- #1

- Feb 14, 2012

- 3,894

Here is this week's POTW:

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$x^3+ax^2+bx+c$ has three distinct real roots, but $(x^2+x+2001)^3+a(x^2+x+2001)^2+b(x^2+x+2001)+c$ has no real roots. Show that $2001^3+a(2001^2)+b(2001)+c>\dfrac{1}{64}$.

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Remember to read the POTW submission guidelines to find out how to submit your answers!

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$x^3+ax^2+bx+c$ has three distinct real roots, but $(x^2+x+2001)^3+a(x^2+x+2001)^2+b(x^2+x+2001)+c$ has no real roots. Show that $2001^3+a(2001^2)+b(2001)+c>\dfrac{1}{64}$.

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Remember to read the POTW submission guidelines to find out how to submit your answers!

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