# Math Contest Problem

• March 12th 2011, 04:23 PM
eric1299171
Math Contest Problem
I would really appreciate any help on this problem! It was from the 2002 Luzerne County Math Contest. How many real roots does x^6 - 6x^3 + x^2 - 2x + 11 possess? No calculator is allowed.
• March 12th 2011, 05:27 PM
skeeter
Quote:

Originally Posted by eric1299171
I would really appreciate any help on this problem! It was from the 2002 Luzerne County Math Contest. How many real roots does x^6 - 6x^3 + x^2 - 2x + 11 possess? No calculator is allowed.

$x^6 - 6x^3 + x^2 - 2x + 11 =$

$x^6 - 6x^3 + 9 + x^2 - 2x + 1 + 1 =$

$(x^3 - 3)^2 + (x - 1)^2 + 1$

what does the last expression tell you about possible real roots?
• March 12th 2011, 05:45 PM
eric1299171
There are no real roots since it is always greater than zero. Thanks for the help! =)