Question

If α and β are the zeros of the quadratic polynomial f(x) = 6x² + x − 2, find the value of `alpha/beta+beta/alpha`.

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)`

= `(1/36 + 2/3)/((-1)/3)`

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

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

= `(-25)/12`

= `alpha/beta + beta/alpha = (-25)/12`