Question

ans it fast iit jee mains que​

Answer 1

$if \: \alpha \: and \: \beta \: are \: the \: roots \: of \: equation \\ \\ a {x}^{2} + bx + c = 0 \\ \\ \alpha + \beta = - \frac{b}{a} \\ \\ \alpha \beta = \frac{c}{a} \\ \\ now \: given \\ \\ 2 {x}^{2} + 3x + 4 = 0 \\ \\ \alpha + \beta = - \frac{3}{2} \\ \\ \alpha \beta = 2 \\ \\ { \alpha }^{2} + { \beta }^{2} \\ \\ = { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta - 2 \alpha \beta \\ \\ {( \alpha + \beta )}^{2} - 2 \alpha \beta \\ \\ = \frac{9}{4} - 4 \\ \\ = - \frac{7}{4} \\ \\ \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } \\ \\ = \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } \\ \\ = \frac{( - \frac{7}{4} )}{2} \\ \\ = - \frac{7}{8}$

hope it helps.