2 The cubic equation \(x ^ { 3 } + 5 x ^ { 2 } + 10 x - 2 = 0\) has roots \(\alpha , \beta , \gamma\).
- Find the value of \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 }\).
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\includegraphics[max width=\textwidth, alt={}, center]{e34e64b7-d3bb-4614-bf37-5ef90ad56157-04_65_1566_573_328}
\includegraphics[max width=\textwidth, alt={}, center]{e34e64b7-d3bb-4614-bf37-5ef90ad56157-04_65_1570_662_324}
\includegraphics[max width=\textwidth, alt={}, center]{e34e64b7-d3bb-4614-bf37-5ef90ad56157-04_65_1570_751_324}
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\includegraphics[max width=\textwidth, alt={}, center]{e34e64b7-d3bb-4614-bf37-5ef90ad56157-04_68_1570_931_324}
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\includegraphics[max width=\textwidth, alt={}]{e34e64b7-d3bb-4614-bf37-5ef90ad56157-04_72_1570_1379_324} ........................................................................................................................................
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\includegraphics[max width=\textwidth, alt={}, center]{e34e64b7-d3bb-4614-bf37-5ef90ad56157-04_74_1572_1921_322}
\includegraphics[max width=\textwidth, alt={}, center]{e34e64b7-d3bb-4614-bf37-5ef90ad56157-04_70_1570_2012_324} - Show that the matrix \(\left( \begin{array} { c c c } 1 & \alpha & \beta
\alpha & 1 & \gamma
\beta & \gamma & 1 \end{array} \right)\) is singular.