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Question
If α and β are the zeros of the quadratic polynomial p(y) = 5y2 − 7y + 1, find the value of `1/alpha+1/beta`
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Solution
Since 𝛼 𝑎𝑛𝑑 𝛽 are the zeroes of the polynomials
p(y) = 5y2 – 7y + 1
Sum of the zeroes `alpha+beta="-coeeficient of x"/("coefficient of "x^2)`
`=-(-7)/5`
`=7/5`
Product of zeroes `=alphabeta="constant term"/"coefficient of "x^2`
`=1/5`
We have, `1/alpha+1/beta=(alpha+beta)/(alphabeta)`
By substituting `alpha+beta=7/5` and `alphabeta=1/5` we get,
`1/alpha+1/beta=(7/5)/(1/5)`
`1/alpha+1/beta=7/5xx5/1`
`1/alpha+1/beta=7`
Hence, the value of `1/alpha+1/beta` is 7
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