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: 1/9 question 2 given the function c(n)=4n^4 - 40n^3 + 84n^2; its c - intercept is its n - intercepts are question help: video written example message instructor submit question

Explanation:

Step1: Find the C - intercept

Set \(n = 0\) in \(C(n)=4n^{4}-40n^{3}+84n^{2}\). 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 \(4n^{2}\): \(4n^{2}(n^{2}-10n + 21)=0\).

Step3: Solve the factored equations

First, \(4n^{2}=0\) gives \(n = 0\). Second, solve \(n^{2}-10n + 21=0\) using the quadratic formula \(n=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\) where \(a = 1\), \(b=-10\), \(c = 21\). \(\Delta=b^{2}-4ac=(-10)^{2}-4\times1\times21=100 - 84 = 16\). Then \(n=\frac{10\pm\sqrt{16}}{2}=\frac{10\pm4}{2}\), so \(n=\frac{10 + 4}{2}=7\) and \(n=\frac{10-4}{2}=3\).

Answer:

C - intercept: \(0\)
n - intercepts: \(0,3,7\)