a,b,c are real.Let alpha,beta be the roots of ax^2+bx+c=0.Express the roots of a^3x^2+abcx+c^3=0 in terms of alpha and beta.a is not equal to zero

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Please find below the solution to the asked query:

We haveax2+bx+c=0α+β=-baαβ=caa3x2+abcx+c3=0Divide by a3x2+abca3x+ca3=0x2+b acax+ca3=0x2-α+βαβx+αβ3=0x2-α2β+αβ2x+α2β.αβ2=0On comparing with x2-Sum of rootsx+Product of roots=0, we get thatroots are α2β,αβ2

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