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# the roots of 3x^2 -2x-5=0 are alpha and beta find the equation whose roots are alpha^2 and beta^2 (Posted for sacha)

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

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