Q.11 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 5–16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between - 10 and 10.$-x^3- \frac{5}{3}{x}^2+ \frac{7}{2} x + 2 = 0$

Step-by-Step Solution

Answer

The values of X are approximately$x\approx \hspace{0.17em}-0.49056\dots ,\hspace{0.17em}x\approx \hspace{0.17em}1.51498\dots ,\hspace{0.17em}x\approx \hspace{0.17em}-2.69108\dots$

Step 1. Given equation and simplification

$$\begin{gathered} -x^3- \frac{5}{3}{x}^2+ \frac{7}{2} x + 2 = 0 \\ \Rightarrow -6x^3-10x^2+21x+12=0 \end{gathered}$$

Step 2.Graph and X-intersection

X-intercepts are $x\approx \hspace{0.17em}-0.49056\dots ,\hspace{0.17em}x\approx \hspace{0.17em}1.51498\dots ,\hspace{0.17em}x\approx \hspace{0.17em}-2.69108\dots$