If `alpha` and `beta` are the zeroes of the polynomial `ax^2+bx+c`, find `(i) alpha^2-beta^2.` `(ii) alpha^3-beta^3`

Explanation

`1)alpha+beta=-b/a`

`alphabeta=c/a`

`alpha^2-beta^2=(alpha+beta)(alpha-beta)`

`=(alpha+beta)sqrt((alpha+bbeta)^2-4alphabeta)`

`alpha^2-beta^2=(-b/a)(sqrt(b^2/a^2-(4c)/a))`

`=-b/asqrt((b^2-4ac)/a^2)`

`=-b/asqrt(b^2-4ac)`

2)`alpha^3-beta^3=(alpha-beta)
(alpha^2+beta^2+alphabeta)`

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