5.5E: Zeros of Polynomial Functions (Exercises)
- Page ID
- 56083
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation.
25. \(2 x^{3}-3 x^{2}-18 x-8=0\)
26. \(3 x^{3}+11 x^{2}+8 x-4=0\)
27. \(2 x^{4}-17 x^{3}+46 x^{2}-43 x+12=0\)
28. \(4 x^{4}+8 x^{3}+19 x^{2}+32 x+12=0\)
For the following exercises, use Descartes' Rule of Signs to find the possible number of positive and negative solutions.
29. \(x^{3}-3 x^{2}-2 x+4=0\)
30. \(2 x^{4}-x^{3}+4 x^{2}-5 x+1=0\)