Question

if alpha and beta are roots of quadratic equation x2-3x-2=0, then alpha/beta +beta/alpha = ?

Answer 1

$\alpha = 3 \\ \beta = - 1$
$\alpha \div \beta + \beta \div \alpha$
=3/-1+-1/3
=3
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Answer 2

x² - 3x - 2 = 0

Sum of zeroes = alpha + beta = - b / a

= + 3 / 1 = 3

Product of zeroes = alpha * beta = c / a

= - 2 / 1 = - 2

Now

$\frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha} \\ \\ \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } \\ \\ \frac{ (\alpha + \beta)² - 2 \alpha \beta }{ \alpha \beta } \\ \\ \frac{3² - 2( - 2)}{ - 2} \\ \\ \frac{9 + 4}{ - 2 } \\ \\ \frac{ 13}{2}$
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