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The sum of all real, non-negative roots is:
+ 4 + 9 = \boxed{13}
Question: A surgical robot's precision function is modeled by $ P(u) = u - \frac{u^3}{3} $. If $ c_n $ is defined by $ c_1 = 1 $ and $ c_{n+1} = P(c_n) $, find $ c_3 $.
Solution: Start with $ c_1 = 1 $ and compute:
$ c_2 = P(1) = 1 - \frac{1^3}{3} = 1 - \frac{1}{3} = \frac{2}{3} $
$ c_3 = P\left(\frac{2}{3}\right) = \frac{2}{3} - \frac{\left(\frac{2}{3}\right)^3}{3} = \frac{2}{3} - \frac{8}{81} = \frac{54 - 8}{81} = \frac{46}{81} $
Thus, the value of $ c_3 $ is:
\boxed{\frac{46}{81}}
$$**Question:** A plant biologist is analyzing a genetic sequence pattern where the number of specific genetic markers appears in a recurring sequence: 5, 11, 17, 23, ... How many such markers will be present in the first 100 terms of this sequence?
Solution:** The sequence given is an arithmetic sequence where the first term \( a = 5 \) and the common difference \( d = 11 - 5 = 6 \).