Let `a ,b ,c` be real numbers with `a!=0 and alpha,beta` be the roots of the equation `a x^2+b x+c=0.` Express the roots of `a^3x^2+a b c x+c^3=0` in terms of `alpha,betadot`

Explanation

`alpha + beta = (-b)/(a), alpha beta = (c) /(a)`
Roots of the equation `a^(3) x^(2) + abcx + c^(3) = 0` are :
`x=(-abcpmsqrt((abc)^(2) - 4a^(2) c^(3)))/(2a^(3))`
`= (-(b)/(a))((c)/(a)) pm(sqrt(((b)/(a))^(2)((c)/(a))^(2) - 4 ((c)/(a))^(3)))/(2)`
`=(alpha beta) (((alpha + beta)pmsqrt((alpha - beta)^(2))))/(2)`
`=alpha beta (((alpha + beta)(alpha - beta)))/(2)`
`alpha^(2) beta, alphabeta^(2)`