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Question
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`
Solution
f(x) = ax2 + bx + c
α + β = `(-b/a)`
αβ = `c/a`
since α + β are the roots (or) zeroes of the given polynomials
then
`1/alpha+1/beta-2alphabeta`
`rArr[(alpha+beta)/alphabeta]-2alphabeta`
`rArr(-b)/axxa/c-2c/b=-2c/a-b/c=(-ab-2c^2)/(ac)-[b/c+(2c)/a]`
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