Question

Find the x-intercept(s) of f(x) = 3,5 – 823 + 16x. Enter intercept(s) as points. If there is more than one point, enter themas a comma separated list.

Answer 1

The Solution:

Given the function below:

$f(x)=x^5-8x^3+16x$

We are required to find all the x-intercepts of the function f(x).

The x-intercepts are the zeroes of the given function. That is, the values of x when f(x) is zero (0).

$\begin{gathered} \text{ When x=0, f(x) will be zero.} \\ x=0 \\ f(0)=0 \\ \text{ So, (0,0) is an x-intercept.} \end{gathered}$$\begin{gathered} \text{ When x=-2} \\ f(-2)=(-2)^5-8(-2)^3+16(-2) \\ f(-2)=-32+64-32=0 \\ \text{ So, (-2,0) is an x-intercept} \end{gathered}$$\begin{gathered} \text{ When x=2} \\ f(2)=(2^5)-8(2^3)+16(2)=32-64+32=0 \\ \text{ So, (2,0) is an x-intercept} \end{gathered}$

Therefore, the correct answer is

$(0,0),(-2,0),(2,0)$