Question

if α and β are zeroes of polynomial 3x^2- 2x - 7,then find α/β+β/α​

Answer 1

let alpha and beta are the zeroes

sum of the zeroes

$\alpha + \beta = \frac{ - b}{a}$

$\alpha + \beta = \frac{ - ( - 2)}{3}$

$\alpha + \beta = \frac{2}{3} ........(1)$

now

product of the zeroes

$\alpha \beta = \frac{c}{a}$

$\alpha \beta = \frac{ - 7}{3} .......(2)$

to find

$\frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha }$

$\frac{ \alpha + \beta }{ \alpha \beta }$

now putting the values of (1) and (2)

we get

$= \frac{ \frac{2}{3} }{ \frac{ - 7}{3} }$

$= \frac{2}{ - 7}$