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Question
The roots of the equation 2x2 – 7x + 5 = 0 are α and β. Without solving for the roots, find `1/alpha + 1/beta`
Solution
2x2 – 7x + 5 = `x^2 - 7/2x + 5/2` = 0
α + β = `7/2`
αβ = `5/2`
`1/alpha + 1/beta = (beta + alpha)/(alphabeta)`
= `(7/2)/(5/2)`
= `7/5`
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