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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`
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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=(beta-alpha)/(alphabeta)=(-(alpha-beta))/(alphabeta)` ................(i)
From (i) we know that `alpha - beta = sqrt(b^2-4ac)/(2a)`
αβ = `c/a`
Putting the values in the (a) `=-((sqrtb^2-4acxxa)/(axxc))=(-sqrt(b^2-4ac))/c`
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