Chapter SH, Problem 5.25EP

To determine

Find all thezeros of the function using graph.

Answer to Problem 5.25EP

The zeros of the given function are $x=-3,x=2\text{and}x=6$ .

Explanation of Solution

Given:

The given function is $f\left(x\right)=x^3-5x^2-12x+36$ and the graph is given below.

  

Calculation:

A zero of a function $f\left(x\right)$ is any value $c$ such that $f\left(c\right)=0$ . When the function is graphed, the real zeros of the function are the x-intercepts of the graph.

In the given graph

  

The x-intercepts are $\left(-3,0\right),\left(2,0\right)\text{and}\left(6,0\right)$ .

Hence the zeros of the given function are $x=-3,x=2\text{and}x=6$ .