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 Pre-Calculus and Calculus
 Roots and unknown coefficients
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happysharlee
Junior Member

USA
5 Posts

Posted - 01/17/2011 :  11:02:19  Show Profile  Reply with Quote
P(x) = x^4 - 6x - x + kx - 72; x-2 is a factor

So, I used synthetic division and got k=54, and I reduced the polynomial to x - 4x + 54x -72.

By Des Cartes theorem, there should be one other positive root and one negative root.

By the conjugate roots theorem, the possible roots are 72, 36, 24, 18, 12, 9, 8, 6, 4, 3, 2, 1.

I tried to find the Upper/Lower bounds and got -4 as the lower bound and 6 as the upper bound. Am I doing something wrong? nothing seems to be divising out to 0, if that makes sense?

Edited by - happysharlee on 01/17/2011 15:56:00
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Ultraglide
Advanced Member

Canada
299 Posts

Posted - 01/18/2011 :  16:33:14  Show Profile  Reply with Quote
Assuming k=54, I graphed the original function and got 1 negative and 3 positive roots.
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