Q 16 - Precalculus Enhanced with Graphing Utilities

Question

Use a graphing utility to approximate the solutions of each equation rounded to two decimal places. All solutions lie between $-10$ and $10$.

$x^3-5x+3=0$.

Step-by-Step Solution

Answer

The required approximated solutions of the given equation are :-

$-2.49,0.66 and 1.83$.

Step 1. Given Information

We have given the following equation :-

$x^3-5x+3=0$.

We have to solve this equation, by using graphic utility.

Firstly we will draw the graph of this equation.

After the we will examine the roots or zeros of the graphs to estimate the solutions.

The roots or zeros exists where the graph cut the x-axis.

Step 2. Graph the equation

The given equation is :-

$x^3-5x+3=0$.

We can graph the equation by using graphic utility as following :-

Step 3. Approximate Solutions

In the following graph of given function :-

We know that the solution exists, where the graph cuts the x-axis or at zeros of the equation.

We can see that the cuts the x-axis, at three points.

So the approximated solutions of given equation are :-

$-2.49,0.66 and 1.83$.