Answer 1

f(x) = 6𝑥2 − 𝑥 − 2

Since α and β are the zeroes of the given polynomial

∴ Sum of zeroes [α + β] `=(-1)/6`

Product of zeroes `(alphabeta)=(-1)/3`

`=alpha/beta+beta/alpha=(alpha^2+beta^2)/(alphabeta)=((alpha+beta)^2-2alphabeta)/(alphabeta)`

`=((1/6)^2-2xx((-1)/3))/(-1/3)`

`=(1/6-2/3)/(-1/3)`

`=((1+24)/36)/(-1/3)`

`=(25/36)/(-1/3)`

`=-25/12`