Question

homework assignment 5.3 graphs of polynomial functions due friday by 11:59pm points 9 submitting an external tool homework assignment 5.3 graphs of polynomial functions score: 1/9 answered: 2/9 × question 2 score on last try: 0 of 1 pts. see details for more. at least one scored part is incorrect. jump to first changeable incorrect part. > next question get a similar question you can retry this question below given the function c(n)=4n^4 - 40n^3 + 84n^2: its c - intercept is its n - intercepts are

Explanation:

Step1: Find the C - intercept

Set \(n = 0\) in the function \(C(n)=4n^{4}-40n^{3}+84n^{2}\). Then \(C(0)=4\times0^{4}-40\times0^{3}+84\times0^{2}=0\).

Step2: Find the n - intercepts

Set \(C(n)=0\), so \(4n^{4}-40n^{3}+84n^{2}=0\). Factor out \(4n^{2}\): \(4n^{2}(n^{2}-10n + 21)=0\).
Factor the quadratic \(n^{2}-10n + 21=(n - 3)(n - 7)\). Then the equation becomes \(4n^{2}(n - 3)(n - 7)=0\).
Using the zero - product property, if \(4n^{2}=0\), then \(n = 0\); if \(n-3=0\), then \(n = 3\); if \(n - 7=0\), then \(n=7\).

Answer:

The \(C\) - intercept is \(0\).
The \(n\) - intercepts are \(0,3,7\).