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If \alpha,\beta are roots of the equation  x^{2}-4x+10= 0, then  \frac{\alpha }{\beta }+\frac{\beta }{\alpha }  equals

Option: 1

\frac{2}{5}


Option: 2

\frac{8}{5}


Option: 3

\frac{-2}{5}


Option: 4

None of these


Answers (1)

best_answer

\frac{\alpha }{\beta }+\frac{\beta }{\alpha }=\frac{\alpha ^{2}+\beta ^{2}}{\alpha \beta }\\

= \frac{\left ( \alpha +\beta \right )^{2}-2\alpha \beta }{\alpha \beta }\\

= \frac{\left ( 4 \right )^{2}-2\cdot \left ( 10 \right )}{10}\\

= \frac{16-20}{10}\\

= \frac{-4}{10}= \frac{-2}{5}

Posted by

mansi

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