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what are the zeros for 69x^4-2x^3+62x^2-2x-7

 Oct 2, 2014

Best Answer 

 #1
avatar+130511 
+5

 

 

 

 

$${\mathtt{69}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{4}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{62}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{7}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\mathtt{7}}}{{\mathtt{23}}}}\\
{\mathtt{x}} = {\frac{{\mathtt{1}}}{{\mathtt{3}}}}\\
{\mathtt{x}} = -{\mathtt{1}}{i}\\
{\mathtt{x}} = {i}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{0.304\: \!347\: \!826\: \!086\: \!956\: \!5}}\\
{\mathtt{x}} = {\mathtt{0.333\: \!333\: \!333\: \!333\: \!333\: \!3}}\\
{\mathtt{x}} = -{\mathtt{1}}{i}\\
{\mathtt{x}} = {i}\\
\end{array} \right\}$$

 

So, this polynomial has two "real" and two "non-real" roots  !!!

 

 Oct 3, 2014
 #1
avatar+130511 
+5
Best Answer

 

 

 

 

$${\mathtt{69}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{4}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{62}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{7}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\mathtt{7}}}{{\mathtt{23}}}}\\
{\mathtt{x}} = {\frac{{\mathtt{1}}}{{\mathtt{3}}}}\\
{\mathtt{x}} = -{\mathtt{1}}{i}\\
{\mathtt{x}} = {i}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{0.304\: \!347\: \!826\: \!086\: \!956\: \!5}}\\
{\mathtt{x}} = {\mathtt{0.333\: \!333\: \!333\: \!333\: \!333\: \!3}}\\
{\mathtt{x}} = -{\mathtt{1}}{i}\\
{\mathtt{x}} = {i}\\
\end{array} \right\}$$

 

So, this polynomial has two "real" and two "non-real" roots  !!!

 

CPhill Oct 3, 2014

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