Q 6. - Precalculus Enhanced with Graphing Utilities

Question

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

Equation is $-x^3+7x-2=x^2+3x-3$.

Step-by-Step Solution

Answer

The roots of the given equation are $x=-1 ,x=\pm 2$.

Step 1. Given information .

Consider the given equation .$-x^3+7x-2=x^2+3x-3$

Step 2. Find the root of the given equation.

To find the root simplify the given equation.

$$\begin{gathered} -x^3-+7x-2=-x^2-3x+3 \\ {x}^3+x^2-4x-1=0 \\ {x}^2\left(x+1\right)-4\left(x+1\right)=0 \\ x=-1 ,x=\pm 2 \end{gathered}$$

Step 3. Plot the graph.

The graph of the given equation using graphic utility as shown below.

$$\begin{gathered} Y_1=-x^3+7x-2 \\ {Y}_2=x^2+3x-3 \end{gathered}$$