Chapter 9.3, Problem 39PPS

To determine

The solutions of the equation $f\left(x\right)=x^3-3x^2-6x+8$ by graphing and find the zeros to the nearest tenth

Answer to Problem 39PPS

  $x=-2,1,4$

Explanation of Solution

Given:

The function, $f\left(x\right)=x^3-3x^2-6x+8$ .

Concept Used:

The solutions of a quadratic equation are given by the points where the graph of the function intersects the x-axis.

In order find the solutions of the given function $f\left(x\right)=x^3-3x^2-6x+8$ , first plot the graph of the function $y=x^3-3x^2-6x+8$ and identify the zeros of the function.

The zeros of the function are the points where the graph of the function intersects the x-axis.

The graph of the function $y=x^3-3x^2-6x+8$ is shown below,

  

From the above graph of the function it is clear that the zeros of the function occur at the points $\left(-2,0\right),\left(1,0\right)\text{ and }\left(4,0\right)$ .

Thus, the solution to the nearest tenth of x is $x=-2,1,4$