Attachment 18373

Attachment 18372

i understand how four was found. i dont understand how 8/3 was found.

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- Jul 29th 2010, 12:50 AMnando29real zeros of a polynomial function
Attachment 18373

Attachment 18372

i understand how four was found. i dont understand how 8/3 was found. - Jul 29th 2010, 02:37 AMHallsofIvy
$\displaystyle a_0= -\frac{1}{3}$, $\displaystyle a_1= \frac{1}{3}$, $\displaystyle a_2= -\frac{4}{3}$, $\displaystyle a_3= \frac{5}{3}$, and $\displaystyle a_4= -\frac{1}{3}$ again.

Taking absolute values, $\displaystyle |a_0|= \frac{1}{3}$, $\displaystyle |a_1|= \frac{1}{3}$, $\displaystyle |a_2|= \frac{4}{3}$, $\displaystyle |a_3|= \frac{5}{3}$, and $\displaystyle |a_4|= \frac{1}{3}$ so we really only have three different values, $\displaystyle \frac{1}{3}$, $\displaystyle \frac{4}{3}$, and $\displaystyle \frac{5}{3}$.

The largest (max) of those is $\displaystyle \frac{5}{3}$ so $\displaystyle 1+ max(|a_0, a_1, a_2, a_3, a_4)$ is $\displaystyle 1+ \frac{5}{3}= \frac{3}{3}+ \frac{5}{3}= \frac{8}{3}$.

The difference between the two is that in the first one, you add all the fractions, to get 4, then take the larger of 1 and 4. In the second, you take the largest of the fractions, then add 1 to that. - Jul 29th 2010, 02:40 AMtonio
- Jul 29th 2010, 10:34 AMnando29
thank you very much!