+0  
 
+2
366
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avatar+26328 

$${\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{5}} = {\mathtt{0}} = \left\{ \begin{array}{l}{\mathtt{x}} = {\frac{{\mathtt{5}}}{{\mathtt{3}}}}\\
{\mathtt{x}} = -{\mathtt{1}}\\
\end{array} \right\}$$

So alpha = 5/3 and beta = -1

To get the (quadratic) equation whose roots are alpha2 and beta2 we construct:

(x - alpha2)*(x-beta2) = 0   or:

 x2 -(alpha2+beta2)*x + alpha2*beta2 = 0

 

I'll leave you to put the numbers in.

Alan  Apr 22, 2014
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Wow Very Cmplex Math 

ProMagma  Nov 3, 2017

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