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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`.
Solution
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`
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