Question

If alpha and beta are zeros of p(x)= x^2+x-1 then find alpha/beta +beta/alpha

Answer 1

$from \: \: the \: \: polynomial \\ \alpha + \beta = - 1 \: \: \: and \: \: \: \alpha \beta = - 1 \\ \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } = \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } \\ = \frac{ {( \alpha + \beta )}^{2} - 2 \alpha \beta }{ \alpha \beta } \\ = \frac{ {( - 1)}^{2} - 2 \times - 1}{ - 1} = \frac{1 + 2}{ - 1} = - 3$