Question

X2-x-4 if alpha and beta are zeroes find value of alpha/beta+beta / alpha

Answer 1

${x}^{2} - x - 4 = 0 \\ \alpha \beta = - 4 \\ \alpha + \beta = 1 \\ { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta = 1 \\ { \alpha }^{2} + { \beta }^{2} + 2 \times ( - 4) = 1 \\ { \alpha }^{2} + { \beta }^{2} = 9$
Now
$\frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } \\ = \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } \\ = \frac{9}{ - 4} \\ = \frac{ - 9}{4}$