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 Roots and unknown coefficients

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T O P I C    R E V I E W
happysharlee Posted - 01/17/2011 : 11:02:19
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?
1   L A T E S T    R E P L I E S    (Newest First)
Ultraglide Posted - 01/18/2011 : 16:33:14
Assuming k=54, I graphed the original function and got 1 negative and 3 positive roots.

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