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In the quadratic equation ax^2 + bx + c ...

In the quadratic equation `ax^2 + bx + c = 0`, if `Delta = b^2-4ac and alpha + beta, alpha^2 + beta^2, alpha^3 + beta^3` are in GP. where `alpha, beta` are the roots of `ax^2 + bx + c =0`, then

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`ax^2 + bx+c = 0`
`alpha and beta` are roots
`alpha + beta = -b/a`
`alpha*beta= c/a`
given, `/_ = b^2- 4ac`
& `alpha+ beta , alpha^2+beta^2, alpha^3+ beta^3` are in GP.
:. the condition will be
`(alpha^2 + beta^2)^2 = (alpha+ beta)*(alpha^3+ beta^3)`
...
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