Q.12. - 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.$-x^4 + 3x^3+ \frac{7}{3} x^2 - \frac{15}{2} x + 2 = 0$

Step-by-Step Solution

Answer

The values of X are approximately $x\approx \hspace{0.17em}0.30612\dots ,\hspace{0.17em}x\approx \hspace{0.17em}1.31422\dots ,\hspace{0.17em}x\approx \hspace{0.17em}-1.64406\dots ,\hspace{0.17em}x\approx \hspace{0.17em}3.02370\dots$

Step 1.Given equation and siplification

$$\begin{gathered} -x^4+3x^3+\frac{7}{3}{x}^2-\frac{15}{2}x+2=0 \\ -6x^4+18x^3+14x^2-45x+12=0 \end{gathered}$$

Step 2. Graph and X-intercepts

X- intercepts are $x\approx \hspace{0.17em}0.30612\dots ,\hspace{0.17em}x\approx \hspace{0.17em}1.31422\dots ,\hspace{0.17em}x\approx \hspace{0.17em}-1.64406\dots ,\hspace{0.17em}x\approx \hspace{0.17em}3.02370\dots$