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If alpha, beta are the roots of a x^2 + ...

If `alpha, beta` are the roots of `a x^2 + 2bx + c = 0` then `alpha/beta + beta/alpha` =

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As `alpha` and `beta` are the roots of `ax^2+2bx+c = 0`,
`:. alpha+beta = -(2b)/a`
`alphabeta = c/a`
Now, `alpha/beta+beta/alpha = (alpha^2+beta^2)/(alphabeta)`
`=((alpha+beta)^2-2alphabeta)/(alphabeta)`
`=((4b^2)/a^2 - (2c)/a)/(c/a)`
`=(4b^2-2ac)/(ac)`
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